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Theorem el2v1 37821
Description: New way (elv 3467, 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 3465 . 2 𝑥 ∈ V
2 el2v1.1 . 2 ((𝑥 ∈ V ∧ 𝜑) → 𝜓)
31, 2mpan 688 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 394  wcel 2098  Vcvv 3461
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3463
This theorem is referenced by:  el3v12  37826  el3v13  37827  exan3  37896  exanres3  37898  ecin0  37954  disjsuc2  37993  eldm1cossres2  38063  brcosscnv  38074  eqvrelqsel  38218
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