Theorem nfmo1 1987

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 1979	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		nfe1 1455	. . 3 |- F/ x E. x ph
3		nfeu1 1986	. . 3 |- F/ x E! x ph
4	2, 3	nfim 1534	. 2 |- F/ x ( E. x ph -> E! x ph )
5	1, 4	nfxfr 1433	1 |- F/ x E* x ph

Syntax hints:   -> wi 4   F/wnf 1419   E.wex 1451   E!weu 1975   E*wmo 1976

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497  ax-i5r 1498

This theorem depends on definitions:  df-bi 116  df-nf 1420  df-eu 1978  df-mo 1979

This theorem is referenced by:  moanmo  2052  euexex  2060  nfrmo1  2577  mob  2835  morex  2837  funimaexglem  5164