Wikipedia:Tutorial (historical)/Citing sources/sandbox

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\exists x\,\forall y\,P(x,y)\Rightarrow \forall y\,\exists x\,P(x,y)\alpha \beta \gamma \mathrm {A}

\forall x\,P(x)\lor \forall x\,Q(x)\Rightarrow \forall x\,(P(x)\lor Q(x))

\exists x\,(P(x)\land Q(x))\Rightarrow \exists x\,P(x)\land \exists x\,Q(x)

\exists x\,P(x)\land \forall x\,Q(x)\Rightarrow \exists x\,(P(x)\land Q(x))

\forall x\,P(x)\Rightarrow P(c)

(If c is a variable, then it must not already be quantified somewhere in P(x))

P(c)\Rightarrow \exists x\,P(x)

(x must not appear free in P(c))