Theorem nfmod 1992

Description: Bound-variable hypothesis builder for "at most one." (Contributed by Mario Carneiro, 14-Nov-2016.)

Hypotheses

Ref	Expression
nfeud.1	|- F/ y ph
nfeud.2	|- ( ph -> F/ x ps )

Assertion

Ref	Expression
nfmod	|- ( ph -> F/ x E* y ps )

Proof of Theorem nfmod

Step	Hyp	Ref	Expression
1		df-mo 1979	. 2 |- ( E* y ps <-> ( E. y ps -> E! y ps ) )
2		nfeud.1	. . . 4 |- F/ y ph
3		nfeud.2	. . . 4 |- ( ph -> F/ x ps )
4	2, 3	nfexd 1717	. . 3 |- ( ph -> F/ x E. y ps )
5	2, 3	nfeud 1991	. . 3 |- ( ph -> F/ x E! y ps )
6	4, 5	nfimd 1547	. 2 |- ( ph -> F/ x ( E. y ps -> E! y ps ) )
7	1, 6	nfxfrd 1434	1 |- ( ph -> F/ x E* y ps )

Syntax hints:   -> wi 4   F/wnf 1419   E.wex 1451   E!weu 1975   E*wmo 1976

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498

This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979

This theorem is referenced by:  nfmo  1995