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Theorem el3v1 34333
Description: New way (elv 34328, 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 3354 . 2 𝑥 ∈ V
2 el3v1.1 . 2 ((𝑥 ∈ V ∧ 𝜓𝜒) → 𝜃)
31, 2mp3an1 1559 1 ((𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1071  wcel 2145  Vcvv 3351
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-12 2203  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-3an 1073  df-tru 1634  df-ex 1853  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-v 3353
This theorem is referenced by:  el3v12  34336  br1cossxrnres  34540
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