Theorem el2v1 36370

Description: New way (elv 3438, 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 3436	. 2 ⊢ 𝑥 ∈ V
2		el2v1.1	. 2 ⊢ ((𝑥 ∈ V ∧ 𝜑) → 𝜓)
3	1, 2	mpan 687	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4   ∧ wa 396   ∈ wcel 2106  Vcvv 3432

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434

This theorem is referenced by:  el3v12  36375  el3v13  36376  exan3  36429  exanres3  36431  ecin0  36484  eldm1cossres2  36579  brcosscnv  36590  eqvrelqsel  36729