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Theorem el2v1 37690
Description: New way (elv 3477, 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 3475 . 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 395  wcel 2099  Vcvv 3471
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473
This theorem is referenced by:  el3v12  37695  el3v13  37696  exan3  37766  exanres3  37768  ecin0  37824  disjsuc2  37863  eldm1cossres2  37933  brcosscnv  37944  eqvrelqsel  38088
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