Theorem nfmo 2475

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 1721	. . 3 ⊢ Ⅎ𝑦⊤
2		nfeu.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmod 2473	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	trud 1484	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1476  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:  mo3  2495  moexex  2529  2moex  2531  2euex  2532  2mo  2539  reusv1  4792  reusv1OLD  4793  reusv2lem1  4794  mosubopt  4897  dffun6f  5818