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 Apr 24 revised Find all possible real solutions. added 4 characters in body; edited title Apr 20 comment Prove that: $\vdash \forall x(\forall y\alpha)\to \forall y(\forall x \alpha)$ So the swap is not possible if x and y are free in alpha, right? Coz you have used that x and y are not free in alpha. @MauroALLEGRANZA Apr 20 comment Prove that: $\vdash \forall x \exists !y(y=x)$ Can you exactly state which axiom you have used where? The first axiom states that $\forall x(x=x)$. How have you used it here? Apr 20 comment Prove that: $\vdash \forall x \exists !y(y=x)$ That is intuitively obvious but I am not able to prove it formally in first order logic @Farnight. Apr 20 asked Prove that: $\vdash \forall x \exists !y(y=x)$ Apr 20 comment Prove that: $\vdash \forall x(\forall y\alpha)\to \forall y(\forall x \alpha)$ That is what troubles me. I can say something only if x and y are free in α. Apr 20 asked Prove that: $\vdash \forall x(\forall y\alpha)\to \forall y(\forall x \alpha)$ Apr 19 reviewed Close $\frac{1+\sqrt[3]{\tan x}}{1-2(\cos^2 x)}$ Apr 19 reviewed Approve $\frac{1+\sqrt[3]{\tan x}}{1-2(\cos^2 x)}$ Apr 19 asked How do I prove that $\vDash \alpha \to \forall x\alpha$, if $x$ is not free in $\alpha$ Apr 19 reviewed No Action Needed covariance of random variables Apr 19 reviewed Looks OK Continuity of $f(x,y,z)=1/(x+y+z-\sqrt{3})$ Mar 25 reviewed No Action Needed Completing this specific integral Mar 25 comment Prove $\cos(2\theta) + \cos\left(2 \left(\frac{\pi}{3} + \theta\right)\right) +\cos\left(2 \left(\frac{2\pi}{3} + \theta\right)\right) = 0$ Do you know about complex numbers? Mar 25 reviewed Approve Prove $\cos(2\theta) + \cos\left(2 \left(\frac{\pi}{3} + \theta\right)\right) +\cos\left(2 \left(\frac{2\pi}{3} + \theta\right)\right) = 0$ Mar 25 reviewed Reviewed Which of the following function(s) has/have removable discontinuity at $x=1?$ Mar 24 reviewed Approve Sum of digits produced by a function show repeating numbers/sequences, why? Mar 24 revised Finding the Locus of Circumcentre added 2 characters in body Mar 22 revised Open cover, finite subcover added 9 characters in body Mar 22 revised Help with linear differential equation problem added 54 characters in body