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Theorem el3v23 35656
Description: New way (elv 3449, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 11-Jul-2021.)
Hypothesis
Ref Expression
el3v23.1 ((𝜑𝑦 ∈ V ∧ 𝑧 ∈ V) → 𝜃)
Assertion
Ref Expression
el3v23 (𝜑𝜃)

Proof of Theorem el3v23
StepHypRef Expression
1 el3v23.1 . . 3 ((𝜑𝑦 ∈ V ∧ 𝑧 ∈ V) → 𝜃)
21el3v3 35653 . 2 ((𝜑𝑦 ∈ V) → 𝜃)
32elvd 3450 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1084  wcel 2112  Vcvv 3444
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 2114  ax-9 2122  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446
This theorem is referenced by:  brxrn2  35786
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