Theorem el3v3

Description: If a proposition is implied by z e. _V (which is true, see vex ) and two other antecedents, then it is implied by these other antecedents. New way ( elv , and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020)

	Ref	Expression
Hypothesis	el3v3.1	|- ( ( ph /\ ps /\ z e. _V ) -> th )
Assertion	el3v3	|- ( ( ph /\ ps ) -> th )

Proof

Step	Hyp	Ref	Expression
1		el3v3.1	|- ( ( ph /\ ps /\ z e. _V ) -> th )
2		vex	|- z e. _V
3	2 1	mp3an3	|- ( ( ph /\ ps ) -> th )