Theorem nfmo 2065

Description: Bound-variable hypothesis builder for "at most one". (Contributed by NM, 9-Mar-1995.)

Hypothesis

Ref	Expression
nfeu.1	|- F/ x ph

Assertion

Ref	Expression
nfmo	|- F/ x E* y ph

Proof of Theorem nfmo

Step	Hyp	Ref	Expression
1		nftru 1480	. . 3 |- F/ y T.
2		nfeu.1	. . . 4 |- F/ x ph
3	2	a1i 9	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfmod 2062	. 2 |- ( T. -> F/ x E* y ph )
5	4	mptru 1373	1 |- F/ x E* y ph

Syntax hints:   T. wtru 1365   F/wnf 1474   E*wmo 2046

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-eu 2048  df-mo 2049

This theorem is referenced by:  euexex  2130  nfdisjv  4022  reusv1  4493  mosubopt  4728  dffun6f  5271