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Theorem ssrmof 3166
 Description: "At most one" existential quantification restricted to a subclass. (Contributed by Thierry Arnoux, 8-Oct-2017.)
Hypotheses
Ref Expression
ssrexf.1
ssrexf.2
Assertion
Ref Expression
ssrmof

Proof of Theorem ssrmof
StepHypRef Expression
1 ssrexf.1 . . . . 5
2 ssrexf.2 . . . . 5
31, 2dfss2f 3094 . . . 4
43biimpi 119 . . 3
5 pm3.45 587 . . . 4
65alimi 1432 . . 3
7 moim 2064 . . 3
84, 6, 73syl 17 . 2
9 df-rmo 2425 . 2
10 df-rmo 2425 . 2
118, 9, 103imtr4g 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wal 1330   wcel 1481  wmo 2001  wnfc 2269  wrmo 2420   wss 3077 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  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rmo 2425  df-in 3083  df-ss 3090 This theorem is referenced by: (None)
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