Theorem el3v2 38167

Description: New way (elv 3469, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020.)

Hypothesis

Ref	Expression
el3v2.1	⊢ ((𝜑 ∧ 𝑦 ∈ V ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
el3v2	⊢ ((𝜑 ∧ 𝜒) → 𝜃)

Proof of Theorem el3v2

Step	Hyp	Ref	Expression
1		vex 3468	. 2 ⊢ 𝑦 ∈ V
2		el3v2.1	. 2 ⊢ ((𝜑 ∧ 𝑦 ∈ V ∧ 𝜒) → 𝜃)
3	1, 2	mp3an2 1450	1 ⊢ ((𝜑 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086   ∈ wcel 2107  Vcvv 3464

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-v 3466

This theorem is referenced by: (None)