Theorem nfmo1 2098

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 2090	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		nfe1 1549	. . 3 |- F/ x E. x ph
3		nfeu1 2097	. . 3 |- F/ x E! x ph
4	2, 3	nfim 1625	. 2 |- F/ x ( E. x ph -> E! x ph )
5	1, 4	nfxfr 1527	1 |- F/ x E* x ph

Syntax hints:   -> wi 4   F/wnf 1513   E.wex 1545   E!weu 2086   E*wmo 2087

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-ial 1587  ax-i5r 1588

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-eu 2089  df-mo 2090

This theorem is referenced by:  moanmo  2164  euexex  2172  nfrmo1  2724  mob  3008  morex  3010  funimaexglem  5459