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Theorem ssopab2 4012
 Description: Equivalence of ordered pair abstraction subclass and implication. (Contributed by NM, 27-Dec-1996.) (Revised by Mario Carneiro, 19-May-2013.)
Assertion
Ref Expression
ssopab2

Proof of Theorem ssopab2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfa1 1434 . . . 4
2 nfa1 1434 . . . . . 6
3 sp 1401 . . . . . . 7
43anim2d 320 . . . . . 6
52, 4eximd 1503 . . . . 5
65sps 1430 . . . 4
71, 6eximd 1503 . . 3
87ss2abdv 3013 . 2
9 df-opab 3819 . 2
10 df-opab 3819 . 2
118, 9, 103sstr4g 2986 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wal 1241   wceq 1243  wex 1381  cab 2026   wss 2917  cop 3378  copab 3817 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-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-in 2924  df-ss 2931  df-opab 3819 This theorem is referenced by:  ssopab2b  4013  ssopab2i  4014  ssopab2dv  4015
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