Theorem el3v23 35531

Description: New way (elv 3496, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 11-Jul-2021.)

Hypothesis

Ref	Expression
el3v23.1	⊢ ((𝜑 ∧ 𝑦 ∈ V ∧ 𝑧 ∈ V) → 𝜃)

Assertion

Ref	Expression
el3v23	⊢ (𝜑 → 𝜃)

Proof of Theorem el3v23

Step	Hyp	Ref	Expression
1		el3v23.1	. . 3 ⊢ ((𝜑 ∧ 𝑦 ∈ V ∧ 𝑧 ∈ V) → 𝜃)
2	1	el3v3 35528	. 2 ⊢ ((𝜑 ∧ 𝑦 ∈ V) → 𝜃)
3	2	elvd 3497	1 ⊢ (𝜑 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1082   ∈ wcel 2113  Vcvv 3491

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-ext 2792

This theorem depends on definitions:  df-bi 209  df-an 399  df-3an 1084  df-ex 1780  df-sb 2069  df-clab 2799  df-cleq 2813  df-clel 2892  df-v 3493

This theorem is referenced by:  brxrn2  35661