Theorem nfmod 2473

Description: Bound-variable hypothesis builder for "at most one." (Contributed by Mario Carneiro, 14-Nov-2016.)

Hypotheses

Ref	Expression
nfeud.1	⊢ Ⅎ𝑦𝜑
nfeud.2	⊢ (𝜑 → Ⅎ𝑥𝜓)

Assertion

Ref	Expression
nfmod	⊢ (𝜑 → Ⅎ𝑥∃*𝑦𝜓)

Proof of Theorem nfmod

Step	Hyp	Ref	Expression
1		nfeud.1	. 2 ⊢ Ⅎ𝑦𝜑
2		nfeud.2	. . 3 ⊢ (𝜑 → Ⅎ𝑥𝜓)
3	2	adantr 480	. 2 ⊢ ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → Ⅎ𝑥𝜓)
4	1, 3	nfmod2 2471	1 ⊢ (𝜑 → Ⅎ𝑥∃*𝑦𝜓)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1473  Ⅎwnf 1699  ∃*wmo 2459

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-mo 2463

This theorem is referenced by:  nfmo  2475  wl-mo3t  32537