Theorem el2v1 38767

Description: New way (elv 3468, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 23-Oct-2018.)

Hypothesis

Ref	Expression
el2v1.1	⊢ ((𝑥 ∈ V ∧ 𝜑) → 𝜓)

Assertion

Ref	Expression
el2v1	⊢ (𝜑 → 𝜓)

Proof of Theorem el2v1

Step	Hyp	Ref	Expression
1		vex 3467	. 2 ⊢ 𝑥 ∈ V
2		el2v1.1	. 2 ⊢ ((𝑥 ∈ V ∧ 𝜑) → 𝜓)
3	1, 2	mpan 702	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4   ∧ wa 400   ∈ wcel 2149  Vcvv 3463

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3465

This theorem is referenced by:  el3v12  38770  el3v13  38771  exan3  38838  exanres3  38840  ecin0  38890  disjsuc2  38952  dfpre3  39016  exeupre  39029  preuniqval  39034  eldm1cossres2  39089  brcosscnv  39100  eqvrelqsel  39238  dfpetparts2  39510