Theorem nfmo 2486

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 1727	. . 3 ⊢ Ⅎ𝑦⊤
2		nfeu.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmod 2484	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	trud 1490	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1481  Ⅎwnf 1705  ∃*wmo 2470

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-eu 2473  df-mo 2474

This theorem is referenced by:  mo3  2506  moexex  2540  2moex  2542  2euex  2543  2mo  2550  reusv1  4836  reusv1OLD  4837  reusv2lem1  4838  mosubopt  4942  dffun6f  5871