Theorem el3v1 36372

Description: New way (elv 3438, 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 3436	. 2 ⊢ 𝑥 ∈ V
2		el3v1.1	. 2 ⊢ ((𝑥 ∈ V ∧ 𝜓 ∧ 𝜒) → 𝜃)
3	1, 2	mp3an1 1447	1 ⊢ ((𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1086   ∈ wcel 2106  Vcvv 3432

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1088  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434

This theorem is referenced by:  el3v12  36375  br1cossxrnres  36566