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Theorem el3v1 36792
Description: New way (elv 3472, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020.)
Hypothesis
Ref Expression
el3v1.1 ((𝑥 ∈ V ∧ 𝜓𝜒) → 𝜃)
Assertion
Ref Expression
el3v1 ((𝜓𝜒) → 𝜃)

Proof of Theorem el3v1
StepHypRef Expression
1 vex 3470 . 2 𝑥 ∈ V
2 el3v1.1 . 2 ((𝑥 ∈ V ∧ 𝜓𝜒) → 𝜃)
31, 2mp3an1 1448 1 ((𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1087  wcel 2106  Vcvv 3466
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 2702
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 2709  df-cleq 2723  df-clel 2809  df-v 3468
This theorem is referenced by:  el3v12  36795  br1cossxrnres  37023
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