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Theorem ssopab2 4778
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 1653 . . . 4
43aleximi 1653 . . 3
54ss2abdv 3572 . 2
6 df-opab 4511 . 2
7 df-opab 4511 . 2
85, 6, 73sstr4g 3544 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  {cab 2442  C_wss 3475  <.cop 4035  {copab 4509
This theorem is referenced by:  ssopab2b  4779  ssopab2i  4780  ssopab2dv  4781  opabbrex  6339
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-in 3482  df-ss 3489  df-opab 4511
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