Theorem el3v23 38213

Description: New way (elv 3460, 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 3464	. 2 ⊢ ((𝜑 ∧ 𝑦 ∈ V) → 𝜃)
3	2	elvd 3461	1 ⊢ (𝜑 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1086   ∈ wcel 2109  Vcvv 3455

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 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3457

This theorem is referenced by:  brxrn2  38360