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Theorem ssopab2 4763
 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 id 22 . . . . . 6
21anim2d 565 . . . . 5
32aleximi 1640 . . . 4
43aleximi 1640 . . 3
54ss2abdv 3558 . 2
6 df-opab 4496 . 2
7 df-opab 4496 . 2
85, 6, 73sstr4g 3530 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369  wal 1381   wceq 1383  wex 1599  cab 2428   wss 3461  cop 4020  copab 4494 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-in 3468  df-ss 3475  df-opab 4496 This theorem is referenced by:  ssopab2b  4764  ssopab2i  4765  ssopab2dv  4766  opabbrex  6324
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