Theorem nfmod2 2483

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

Hypotheses

Ref	Expression
nfmod2.1	|- F/ y ph
nfmod2.2	|- ( ( ph /\ -. A. x x = y ) -> F/ x ps )

Assertion

Ref	Expression
nfmod2	|- ( ph -> F/ x E* y ps )

Proof of Theorem nfmod2

Step	Hyp	Ref	Expression
1		df-mo 2475	. 2 |- ( E* y ps <-> ( E. y ps -> E! y ps ) )
2		nfmod2.1	. . . 4 |- F/ y ph
3		nfmod2.2	. . . 4 |- ( ( ph /\ -. A. x x = y ) -> F/ x ps )
4	2, 3	nfexd2 2332	. . 3 |- ( ph -> F/ x E. y ps )
5	2, 3	nfeud2 2482	. . 3 |- ( ph -> F/ x E! y ps )
6	4, 5	nfimd 1823	. 2 |- ( ph -> F/ x ( E. y ps -> E! y ps ) )
7	1, 6	nfxfrd 1780	1 |- ( ph -> F/ x E* y ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 384   A.wal 1481   E.wex 1704   F/wnf 1708   E!weu 2470   E*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475

This theorem is referenced by:  nfmod  2485  nfrmod  3113  nfrmo  3115  nfdisj  4632