Theorem nfmo 2221

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 1554	. . 3 ⊢ Ⅎy ⊤
2		nfeu.1	. . . 4 ⊢ Ⅎxφ
3	2	a1i 10	. . 3 ⊢ ( ⊤ → Ⅎxφ)
4	1, 3	nfmod 2219	. 2 ⊢ ( ⊤ → Ⅎx∃*yφ)
5	4	trud 1323	1 ⊢ Ⅎx∃*yφ

Syntax hints:   ⊤ wtru 1316  Ⅎwnf 1544  ∃*wmo 2205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-eu 2208  df-mo 2209

This theorem is referenced by:  moexex  2273  2moex  2275  2euex  2276  mosubopt  4612  dffun6f  5123