Theorem el3v12 38881

Description: New way (elv 3460, 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 38879	. 2 ⊢ ((𝑦 ∈ V ∧ 𝜒) → 𝜃)
3	2	el2v1 38878	1 ⊢ (𝜒 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1103   ∈ wcel 2143  Vcvv 3455

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-3an 1105  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457

This theorem is referenced by:  ralmo  39009