Theorem nfmod 2070

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 2057	. 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 1783	. . 3 |- ( ph -> F/ x E. y ps )
5	2, 3	nfeud 2069	. . 3 |- ( ph -> F/ x E! y ps )
6	4, 5	nfimd 1607	. 2 |- ( ph -> F/ x ( E. y ps -> E! y ps ) )
7	1, 6	nfxfrd 1497	1 |- ( ph -> F/ x E* y ps )

Syntax hints:   -> wi 4   F/wnf 1482   E.wex 1514   E!weu 2053   E*wmo 2054

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 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-eu 2056  df-mo 2057

This theorem is referenced by:  nfmo  2073