Theorem nfmod 2020

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 2007	. 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 1738	. . 3 |- ( ph -> F/ x E. y ps )
5	2, 3	nfeud 2019	. . 3 |- ( ph -> F/ x E! y ps )
6	4, 5	nfimd 1562	. 2 |- ( ph -> F/ x ( E. y ps -> E! y ps ) )
7	1, 6	nfxfrd 1452	1 |- ( ph -> F/ x E* y ps )

Syntax hints:   -> wi 4   F/wnf 1437   E.wex 1469   E!weu 2003   E*wmo 2004

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 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-eu 2006  df-mo 2007

This theorem is referenced by:  nfmo  2023