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Theorem el3v23 35378
Description: New way (elv 3497, 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 35375 . 2 ((𝜑𝑦 ∈ V) → 𝜃)
32elvd 3498 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1079  wcel 2105  Vcvv 3492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-3an 1081  df-ex 1772  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-v 3494
This theorem is referenced by:  brxrn2  35507
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