Theorem el3v13 37696

Description: New way (elv 3477, 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 37694	. 2 ⊢ ((𝑥 ∈ V ∧ 𝜓) → 𝜃)
3	2	el2v1 37690	1 ⊢ (𝜓 → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1085   ∈ wcel 2099  Vcvv 3471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699

This theorem depends on definitions:  df-bi 206  df-an 396  df-3an 1087  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473

This theorem is referenced by: (None)