Theorem el3v

Description: If a proposition is implied by x e.V , y e. V and z e.V (which is true, see vex ), then it is true. Inference forms (with |- A e. V , |- B e.V and |- C e. V hypotheses) of the general theorems (proving |- ( ( A e. V /\ B e. W /\ C e. X ) -> assertions) may be superfluous. (Contributed by Peter Mazsa, 13-Oct-2018)

	Ref	Expression
Hypothesis	el3v.1	$$⊢\left(x\in \mathrm{V}\wedge y\in \mathrm{V}\wedge z\in \mathrm{V}\right)\to \phi$$
Assertion	el3v	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		el3v.1	$$⊢\left(x\in \mathrm{V}\wedge y\in \mathrm{V}\wedge z\in \mathrm{V}\right)\to \phi$$
2		vex	$$⊢x\in \mathrm{V}$$
3		vex	$$⊢y\in \mathrm{V}$$
4		vex	$$⊢z\in \mathrm{V}$$
5	2 3 4 1	mp3an	$$⊢\phi$$