Theorem nfmo 1902

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 1335	. . 3 ⊢ Ⅎy ⊤
2		nfeu.1	. . . 4 ⊢ Ⅎxφ
3	2	a1i 9	. . 3 ⊢ ( ⊤ → Ⅎxφ)
4	1, 3	nfmod 1899	. 2 ⊢ ( ⊤ → Ⅎx∃*yφ)
5	4	trud 1237	1 ⊢ Ⅎx∃*yφ

Syntax hints:   ⊤ wtru 1229  Ⅎwnf 1329  ∃*wmo 1883

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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410

This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-eu 1885  df-mo 1886

This theorem is referenced by:  euexex  1967  nfdisjv  3731  reusv1  4140  mosubopt  4332  dffun6f  4841