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Theorem mo4 2061
Description: "At most one" expressed using implicit substitution. (Contributed by NM, 26-Jul-1995.)
Hypothesis
Ref Expression
mo4.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
mo4  |-  ( E* x ph  <->  A. x A. y ( ( ph  /\ 
ps )  ->  x  =  y ) )
Distinct variable groups:    x, y    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem mo4
StepHypRef Expression
1 nfv 1509 . 2  |-  F/ x ps
2 mo4.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
31, 2mo4f 2060 1  |-  ( E* x ph  <->  A. x A. y ( ( ph  /\ 
ps )  ->  x  =  y ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104   A.wal 1330   E*wmo 2001
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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004
This theorem is referenced by:  eu4  2062  rmo4  2880  dffun5r  5142  dffun6f  5143  fun11  5197  brprcneu  5421  dff13  5676  mpofun  5880  caovimo  5971  th3qlem1  6538  addnq0mo  7278  mulnq0mo  7279  addsrmo  7574  mulsrmo  7575  summodc  11183  prodmodc  11378  limcimo  12840
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