Theorem el3v1 38939

Description: New way (elv 3462, 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 3461	. 2 ⊢ 𝑥 ∈ V
2		el3v1.1	. 2 ⊢ ((𝑥 ∈ V ∧ 𝜓 ∧ 𝜒) → 𝜃)
3	1, 2	mp3an1 1477	1 ⊢ ((𝜓 ∧ 𝜒) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103   ∈ wcel 2146  Vcvv 3457

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459

This theorem is used by:  el3v12  38941  br1cossxrnres  39247