Theorem el3v3 37084

Description: New way (elv 3480, 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 3478	. 2 ⊢ 𝑧 ∈ V
2		el3v3.1	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝑧 ∈ V) → 𝜃)
3	1, 2	mp3an3 1450	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1087   ∈ wcel 2106  Vcvv 3474

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1089  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476

This theorem is referenced by:  el3v13  37086  el3v23  37087