Theorem el3v12 38731

Description: New way (elv 3459, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 11-Jul-2021.)

Hypothesis

Ref	Expression
el3v12.1	⊢ ((𝑥 ∈ V ∧ 𝑦 ∈ V ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
el3v12	⊢ (𝜒 → 𝜃)

Proof of Theorem el3v12

Step	Hyp	Ref	Expression
1		el3v12.1	. . 3 ⊢ ((𝑥 ∈ V ∧ 𝑦 ∈ V ∧ 𝜒) → 𝜃)
2	1	el3v1 38729	. 2 ⊢ ((𝑦 ∈ V ∧ 𝜒) → 𝜃)
3	2	el2v1 38728	1 ⊢ (𝜒 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1098   ∈ wcel 2142  Vcvv 3454

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734

This theorem depends on definitions:  df-bi 209  df-an 400  df-3an 1100  df-tru 1563  df-ex 1800  df-sb 2091  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456

This theorem is referenced by:  ralmo  38859