Theorem el3v12 35489

Description: New way (elv 3500, 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 35486	. 2 ⊢ ((𝑦 ∈ V ∧ 𝜒) → 𝜃)
3	2	el2v1 35484	1 ⊢ (𝜒 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1083   ∈ wcel 2110  Vcvv 3495

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 3497

This theorem is referenced by: (None)