Theorem el3v23 38262

Description: New way (elv 3441, 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 3445	. 2 ⊢ ((𝜑 ∧ 𝑦 ∈ V) → 𝜃)
3	2	elvd 3442	1 ⊢ (𝜑 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1086   ∈ wcel 2111  Vcvv 3436

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438

This theorem is referenced by:  brxrn2  38403