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Theorem ssoprab2 5592
 Description: Equivalence of ordered pair abstraction subclass and implication. Compare ssopab2 4038. (Contributed by FL, 6-Nov-2013.) (Proof shortened by Mario Carneiro, 11-Dec-2016.)
Assertion
Ref Expression
ssoprab2

Proof of Theorem ssoprab2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 id 19 . . . . . . . . . 10
21anim2d 330 . . . . . . . . 9
32alimi 1385 . . . . . . . 8
4 exim 1531 . . . . . . . 8
53, 4syl 14 . . . . . . 7
65alimi 1385 . . . . . 6
7 exim 1531 . . . . . 6
86, 7syl 14 . . . . 5
98alimi 1385 . . . 4
10 exim 1531 . . . 4
119, 10syl 14 . . 3
1211ss2abdv 3068 . 2
13 df-oprab 5547 . 2
14 df-oprab 5547 . 2
1512, 13, 143sstr4g 3041 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102  wal 1283   wceq 1285  wex 1422  cab 2068   wss 2974  cop 3409  coprab 5544 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-in 2980  df-ss 2987  df-oprab 5547 This theorem is referenced by:  ssoprab2b  5593
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