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Theorem ssopab2 4712
 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 1788 . . . 4
2 nfa1 1788 . . . . . 6
3 sp 1747 . . . . . . 7
43anim2d 548 . . . . . 6
52, 4eximd 1770 . . . . 5
65sps 1754 . . . 4
71, 6eximd 1770 . . 3
87ss2abdv 3339 . 2
9 df-opab 4623 . 2
10 df-opab 4623 . 2
118, 9, 103sstr4g 3312 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wal 1540  wex 1541   wceq 1642  cab 2339   wss 3257  cop 4561  copab 4622 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-opab 4623 This theorem is referenced by:  ssopab2b  4713  ssopab2i  4714  ssopab2dv  4715
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