Theorem nfmo 2097

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 1512	. . 3 |- F/ y T.
2		nfeu.1	. . . 4 |- F/ x ph
3	2	a1i 9	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfmod 2094	. 2 |- ( T. -> F/ x E* y ph )
5	4	mptru 1404	1 |- F/ x E* y ph

Syntax hints:   T. wtru 1396   F/wnf 1506   E*wmo 2078

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-eu 2080  df-mo 2081

This theorem is referenced by:  euexex  2163  nfdisjv  4071  reusv1  4549  mosubopt  4784  dffun6f  5331