Theorem el3v12 38180

Description: New way (elv 3493, 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 38178	. 2 ⊢ ((𝑦 ∈ V ∧ 𝜒) → 𝜃)
3	2	el2v1 38177	1 ⊢ (𝜒 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1087   ∈ wcel 2108  Vcvv 3488

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490

This theorem is referenced by: (None)