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Theorem mo4 1939
Description: "At most one" expressed using implicit substitution. (Contributed by NM, 26-Jul-1995.)
Hypothesis
Ref Expression
mo4.1 (x = y → (φψ))
Assertion
Ref Expression
mo4 (∃*xφxy((φ ψ) → x = y))
Distinct variable groups:   x,y   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem mo4
StepHypRef Expression
1 nfv 1398 . 2 xψ
2 mo4.1 . 2 (x = y → (φψ))
31, 2mo4f 1938 1 (∃*xφxy((φ ψ) → x = y))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98  wal 1224  ∃*wmo 1879
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-sb 1624  df-eu 1881  df-mo 1882
This theorem is referenced by:  eu4  1940  rmo4  2707  dffun6f  4837  fun11  4888  brprcneu  5092  dff13  5328  mpt2fun  5522  caovimo  5613  th3qlem1  6115  addnq0mo  6296  mulnq0mo  6297  addsrmo  6487  mulsrmo  6488
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