Metamath Proof Explorer

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 φ x V ψ
Assertion elvd φ ψ


Step Hyp Ref Expression
1 elvd.1 φ x V ψ
2 vex x V
3 2 1 mpan2 φ ψ