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Theorem el2v1 34637
 Description: New way (elv 3402, 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 3401 . 2 𝑥 ∈ V
2 el2v1.1 . 2 ((𝑥 ∈ V ∧ 𝜑) → 𝜓)
31, 2mpan 680 1 (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 386   ∈ wcel 2107  Vcvv 3398 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-12 2163  ax-ext 2754 This theorem depends on definitions:  df-bi 199  df-an 387  df-tru 1605  df-ex 1824  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-v 3400 This theorem is referenced by:  el3v12  34642  el3v13  34643  exan3  34702  exanres3  34704  ecin0  34754  eldm1cossres2  34848  brcosscnv  34859  eqvrelqsel  35000
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