Theorem nfmo1 2067

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 2059	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		nfe1 1520	. . 3 |- F/ x E. x ph
3		nfeu1 2066	. . 3 |- F/ x E! x ph
4	2, 3	nfim 1596	. 2 |- F/ x ( E. x ph -> E! x ph )
5	1, 4	nfxfr 1498	1 |- F/ x E* x ph

Syntax hints:   -> wi 4   F/wnf 1484   E.wex 1516   E!weu 2055   E*wmo 2056

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-ial 1558  ax-i5r 1559

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-eu 2058  df-mo 2059

This theorem is referenced by:  moanmo  2133  euexex  2141  nfrmo1  2681  mob  2962  morex  2964  funimaexglem  5376