Theorem el3v23 38170

Description: New way (elv 3469, 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 3473	. 2 ⊢ ((𝜑 ∧ 𝑦 ∈ V) → 𝜃)
3	2	elvd 3470	1 ⊢ (𝜑 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1086   ∈ wcel 2107  Vcvv 3464

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-v 3466

This theorem is referenced by:  brxrn2  38317