Theorem nfmo1 2026

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 2018	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		nfe1 1484	. . 3 |- F/ x E. x ph
3		nfeu1 2025	. . 3 |- F/ x E! x ph
4	2, 3	nfim 1560	. 2 |- F/ x ( E. x ph -> E! x ph )
5	1, 4	nfxfr 1462	1 |- F/ x E* x ph

Syntax hints:   -> wi 4   F/wnf 1448   E.wex 1480   E!weu 2014   E*wmo 2015

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 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-eu 2017  df-mo 2018

This theorem is referenced by:  moanmo  2091  euexex  2099  nfrmo1  2638  mob  2908  morex  2910  funimaexglem  5271