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Theorem el3v2 36679
Description: New way (elv 3451, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020.)
Hypothesis
Ref Expression
el3v2.1 ((𝜑𝑦 ∈ V ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
el3v2 ((𝜑𝜒) → 𝜃)

Proof of Theorem el3v2
StepHypRef Expression
1 vex 3449 . 2 𝑦 ∈ V
2 el3v2.1 . 2 ((𝜑𝑦 ∈ V ∧ 𝜒) → 𝜃)
31, 2mp3an2 1449 1 ((𝜑𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1087  wcel 2106  Vcvv 3445
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1089  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3447
This theorem is referenced by: (None)
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