Theorem el3v23 38601

Description: New way (elv 3436, 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 3440	. 2 ⊢ ((𝜑 ∧ 𝑦 ∈ V) → 𝜃)
3	2	elvd 3437	1 ⊢ (𝜑 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1092   ∈ wcel 2119  Vcvv 3431

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-3an 1094  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433

This theorem is referenced by:  brxrn2  38751  ecxrn2  38775