Theorem nfmo 2075

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 1490	. . 3 |- F/ y T.
2		nfeu.1	. . . 4 |- F/ x ph
3	2	a1i 9	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfmod 2072	. 2 |- ( T. -> F/ x E* y ph )
5	4	mptru 1382	1 |- F/ x E* y ph

Syntax hints:   T. wtru 1374   F/wnf 1484   E*wmo 2056

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-eu 2058  df-mo 2059

This theorem is referenced by:  euexex  2141  nfdisjv  4047  reusv1  4523  mosubopt  4758  dffun6f  5303