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Theorem mo4 2176
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 1605 . 2  |-  F/ x ps
2 mo4.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
31, 2mo4f 2175 1  |-  ( E* x ph  <->  A. x A. y ( ( ph  /\ 
ps )  ->  x  =  y ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358   A.wal 1527   E*wmo 2144
This theorem is referenced by:  eu4  2182  rmo4  2958  dffun3  5266  fun11  5315  brprcneu  5518  dff13  5783  wemoiso  5855  wemoiso2  5856  mpt2fun  5946  caovmo  6057  th3qlem1  6764  summo  12190  spwmo  14335  hausflimi  17675  vitalilem3  18965  plyexmo  19693  ajmoi  21437  pjhthmo  21881  adjmo  22412  funtransport  24654  funray  24763  funline  24765  lineintmo  24780
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148
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