# Showing validity of a formula in first order logic [duplicate]

So I'm trying to prove the validity of this formula and I am a bit lost, not sure how to start. I know generally speaking a valid formula is one where if all the premises are true, then the conclusion can not be false, but I don't know how to prove this really. any help is appreciated

http://imgur.com/jop9Gq3

## marked as duplicate by Rick Decker, Claude Leibovici, user91500, hardmath, Henning Makholm logic StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jun 29 '16 at 13:04

Convert to the contrapositive:$$\exists y((\exists x.S(x))\implies S(y))$$with $S=\lnot R$, and maybe it's a little easier to analyse. Simply put, if $\exists x.S(x)$, then there exists a $y$ such that the conclusion, $S(y)$ is true, and the formula is valid. If there is no such $x$, then the formula is vacuously true.