Theorem nfmo 2020

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 1443	. . 3 |- F/ y T.
2		nfeu.1	. . . 4 |- F/ x ph
3	2	a1i 9	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfmod 2017	. 2 |- ( T. -> F/ x E* y ph )
5	4	mptru 1341	1 |- F/ x E* y ph

Syntax hints:   T. wtru 1333   F/wnf 1437   E*wmo 2001

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004

This theorem is referenced by:  euexex  2085  nfdisjv  3926  reusv1  4387  mosubopt  4612  dffun6f  5144