Metamath Proof Explorer


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 φ ψ z V θ
Assertion el3v3 φ ψ θ

Proof

Step Hyp Ref Expression
1 el3v3.1 φ ψ z V θ
2 vex z V
3 2 1 mp3an3 φ ψ θ