Theorem nfmo 2556

Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 9-Mar-1995.)

Hypothesis

Ref	Expression
nfeu.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfmo	⊢ Ⅎ𝑥∃*𝑦𝜑

Proof of Theorem nfmo

Step	Hyp	Ref	Expression
1		nftru 1811	. . 3 ⊢ Ⅎ𝑦⊤
2		nfeu.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmod 2554	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	trud 1574	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1565  Ⅎwnf 1789  ∃*wmo 2540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1818  ax-5 1920  ax-6 1986  ax-7 2022  ax-10 2100  ax-11 2115  ax-12 2128  ax-13 2323

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1567  df-ex 1786  df-nf 1791  df-eu 2543  df-mo 2544

This theorem is referenced by:  mo3  2577  moexex  2611  2moex  2613  2euex  2614  2mo  2621  reusv1  4939  reusv1OLD  4940  reusv2lem1  4941  mosubopt  5044  dffun6f  5983