Theorem el3v13 35656

Description: New way (elv 3446, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 11-Jul-2021.)

Hypothesis

Ref	Expression
el3v13.1	⊢ ((𝑥 ∈ V ∧ 𝜓 ∧ 𝑧 ∈ V) → 𝜃)

Assertion

Ref	Expression
el3v13	⊢ (𝜓 → 𝜃)

Proof of Theorem el3v13

Step	Hyp	Ref	Expression
1		el3v13.1	. . 3 ⊢ ((𝑥 ∈ V ∧ 𝜓 ∧ 𝑧 ∈ V) → 𝜃)
2	1	el3v3 35654	. 2 ⊢ ((𝑥 ∈ V ∧ 𝜓) → 𝜃)
3	2	el2v1 35650	1 ⊢ (𝜓 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1084   ∈ wcel 2111  Vcvv 3441

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443

This theorem is referenced by: (None)