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Theorem ssoprab2i 5593
 Description: Inference of operation class abstraction subclass from implication. (Contributed by NM, 11-Nov-1995.) (Revised by David Abernethy, 19-Jun-2012.)
Hypothesis
Ref Expression
ssoprab2i.1
Assertion
Ref Expression
ssoprab2i
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem ssoprab2i
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssoprab2i.1 . . . . 5
21anim2i 324 . . . 4
322eximi 1492 . . 3
43ssopab2i 4014 . 2
5 dfoprab2 5552 . 2
6 dfoprab2 5552 . 2
74, 5, 63sstr4i 2984 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243  wex 1381   wss 2917  cop 3378  copab 3817  coprab 5513 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-opab 3819  df-oprab 5516 This theorem is referenced by: (None)
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