Theorem nfmo1 1953

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 1945	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		nfe1 1425	. . 3 |- F/ x E. x ph
3		nfeu1 1952	. . 3 |- F/ x E! x ph
4	2, 3	nfim 1504	. 2 |- F/ x ( E. x ph -> E! x ph )
5	1, 4	nfxfr 1403	1 |- F/ x E* x ph

Syntax hints:   -> wi 4   F/wnf 1389   E.wex 1421   E!weu 1941   E*wmo 1942

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-ial 1467  ax-i5r 1468

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-eu 1944  df-mo 1945

This theorem is referenced by:  moanmo  2018  euexex  2026  nfrmo1  2526  mob  2774  morex  2776  funimaexglem  5002