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Theorem el2v1 35562
Description: New way (elv 3485, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 23-Oct-2018.)
Hypothesis
Ref Expression
el2v1.1 ((𝑥 ∈ V ∧ 𝜑) → 𝜓)
Assertion
Ref Expression
el2v1 (𝜑𝜓)

Proof of Theorem el2v1
StepHypRef Expression
1 vex 3483 . 2 𝑥 ∈ V
2 el2v1.1 . 2 ((𝑥 ∈ V ∧ 𝜑) → 𝜓)
31, 2mpan 689 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  wcel 2115  Vcvv 3480
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482
This theorem is referenced by:  el3v12  35567  el3v13  35568  exan3  35623  exanres3  35625  ecin0  35678  eldm1cossres2  35773  brcosscnv  35784  eqvrelqsel  35923
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