Theorem nfmo 1917

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 1352	. . 3 ⊢ Ⅎy ⊤
2		nfeu.1	. . . 4 ⊢ Ⅎxφ
3	2	a1i 9	. . 3 ⊢ ( ⊤ → Ⅎxφ)
4	1, 3	nfmod 1914	. 2 ⊢ ( ⊤ → Ⅎx∃*yφ)
5	4	trud 1251	1 ⊢ Ⅎx∃*yφ

Syntax hints:   ⊤ wtru 1243  Ⅎwnf 1346  ∃*wmo 1898

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425

This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901

This theorem is referenced by:  euexex  1982  nfdisjv  3748  reusv1  4156  mosubopt  4348  dffun6f  4858