Theorem nfmo1 2066

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 2058	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		nfe1 1519	. . 3 |- F/ x E. x ph
3		nfeu1 2065	. . 3 |- F/ x E! x ph
4	2, 3	nfim 1595	. 2 |- F/ x ( E. x ph -> E! x ph )
5	1, 4	nfxfr 1497	1 |- F/ x E* x ph

Syntax hints:   -> wi 4   F/wnf 1483   E.wex 1515   E!weu 2054   E*wmo 2055

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-ial 1557  ax-i5r 1558

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-eu 2057  df-mo 2058

This theorem is referenced by:  moanmo  2131  euexex  2139  nfrmo1  2679  mob  2955  morex  2957  funimaexglem  5357