Theorem nfmo1 2057

Description: Bound-variable hypothesis builder for "at most one". (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.)

Assertion

Ref	Expression
nfmo1	|- F/ x E* x ph

Proof of Theorem nfmo1

Step	Hyp	Ref	Expression
1		df-mo 2049	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		nfe1 1510	. . 3 |- F/ x E. x ph
3		nfeu1 2056	. . 3 |- F/ x E! x ph
4	2, 3	nfim 1586	. 2 |- F/ x ( E. x ph -> E! x ph )
5	1, 4	nfxfr 1488	1 |- F/ x E* x ph

Syntax hints:   -> wi 4   F/wnf 1474   E.wex 1506   E!weu 2045   E*wmo 2046

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-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-eu 2048  df-mo 2049

This theorem is referenced by:  moanmo  2122  euexex  2130  nfrmo1  2670  mob  2946  morex  2948  funimaexglem  5341