Theorem el2v1 38224

Description: New way (elv 3485, 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 3484	. 2 ⊢ 𝑥 ∈ V
2		el2v1.1	. 2 ⊢ ((𝑥 ∈ V ∧ 𝜑) → 𝜓)
3	1, 2	mpan 690	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∈ wcel 2108  Vcvv 3480

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 2007  ax-8 2110  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482

This theorem is referenced by:  el3v12  38227  el3v13  38228  exan3  38295  exanres3  38297  ecin0  38353  disjsuc2  38392  eldm1cossres2  38462  brcosscnv  38473  eqvrelqsel  38617