Theorem el3v3 37089

Description: New way (elv 3481, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020.)

Hypothesis

Ref	Expression
el3v3.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝑧 ∈ V) → 𝜃)

Assertion

Ref	Expression
el3v3	⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Proof of Theorem el3v3

Step	Hyp	Ref	Expression
1		vex 3479	. 2 ⊢ 𝑧 ∈ V
2		el3v3.1	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝑧 ∈ V) → 𝜃)
3	1, 2	mp3an3 1451	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 397   ∧ w3a 1088   ∈ wcel 2107  Vcvv 3475

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-3an 1090  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477

This theorem is referenced by:  el3v13  37091  el3v23  37092