Theorem el3v2 35487

Description: New way (elv 3499, 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 3497	. 2 ⊢ 𝑦 ∈ V
2		el3v2.1	. 2 ⊢ ((𝜑 ∧ 𝑦 ∈ V ∧ 𝜒) → 𝜃)
3	1, 2	mp3an2 1445	1 ⊢ ((𝜑 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 398   ∧ w3a 1083   ∈ wcel 2110  Vcvv 3494

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-3an 1085  df-ex 1777  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-v 3496

This theorem is referenced by: (None)