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Theorem el3v13 35614
Description: New way (elv 3474, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 11-Jul-2021.)
Hypothesis
Ref Expression
el3v13.1 ((𝑥 ∈ V ∧ 𝜓𝑧 ∈ V) → 𝜃)
Assertion
Ref Expression
el3v13 (𝜓𝜃)

Proof of Theorem el3v13
StepHypRef Expression
1 el3v13.1 . . 3 ((𝑥 ∈ V ∧ 𝜓𝑧 ∈ V) → 𝜃)
21el3v3 35612 . 2 ((𝑥 ∈ V ∧ 𝜓) → 𝜃)
32el2v1 35608 1 (𝜓𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1084  wcel 2114  Vcvv 3469
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 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-v 3471
This theorem is referenced by: (None)
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