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Theorem el2v1 36378
Description: New way (elv 3435, 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 3433 . 2 𝑥 ∈ V
2 el2v1.1 . 2 ((𝑥 ∈ V ∧ 𝜑) → 𝜓)
31, 2mpan 687 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wcel 2106  Vcvv 3429
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3431
This theorem is referenced by:  el3v12  36383  el3v13  36384  exan3  36437  exanres3  36439  ecin0  36492  eldm1cossres2  36587  brcosscnv  36598  eqvrelqsel  36737
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