Theorem el3v1 37591

Description: New way (elv 3472, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020.)

Hypothesis

Ref	Expression
el3v1.1	⊢ ((𝑥 ∈ V ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
el3v1	⊢ ((𝜓 ∧ 𝜒) → 𝜃)

Proof of Theorem el3v1

Step	Hyp	Ref	Expression
1		vex 3470	. 2 ⊢ 𝑥 ∈ V
2		el3v1.1	. 2 ⊢ ((𝑥 ∈ V ∧ 𝜓 ∧ 𝜒) → 𝜃)
3	1, 2	mp3an1 1444	1 ⊢ ((𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1084   ∈ wcel 2098  Vcvv 3466

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695

This theorem depends on definitions:  df-bi 206  df-an 396  df-3an 1086  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468

This theorem is referenced by:  el3v12  37594  br1cossxrnres  37822