Theorem elvd

Description: If a proposition is implied by x e. _V (which is true, see vex ) and another antecedent, then it is implied by that other antecedent. Deduction associated with elv . (Contributed by Peter Mazsa, 23-Oct-2018)

	Ref	Expression
Hypothesis	elvd.1	|- ( ( ph /\ x e. _V ) -> ps )
Assertion	elvd	|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		elvd.1	|- ( ( ph /\ x e. _V ) -> ps )
2		vex	|- x e. _V
3	2 1	mpan2	|- ( ph -> ps )