Theorem nfmo1 2018

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 2010	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		nfe1 1476	. . 3 |- F/ x E. x ph
3		nfeu1 2017	. . 3 |- F/ x E! x ph
4	2, 3	nfim 1552	. 2 |- F/ x ( E. x ph -> E! x ph )
5	1, 4	nfxfr 1454	1 |- F/ x E* x ph

Syntax hints:   -> wi 4   F/wnf 1440   E.wex 1472   E!weu 2006   E*wmo 2007

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1441  df-eu 2009  df-mo 2010

This theorem is referenced by:  moanmo  2083  euexex  2091  nfrmo1  2629  mob  2894  morex  2896  funimaexglem  5255