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Theorem ssopab2 4472
 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 1806 . . . 4
2 nfa1 1806 . . . . . 6
3 sp 1763 . . . . . . 7
43anim2d 549 . . . . . 6
52, 4eximd 1786 . . . . 5
65sps 1770 . . . 4
71, 6eximd 1786 . . 3
87ss2abdv 3408 . 2
9 df-opab 4259 . 2
10 df-opab 4259 . 2
118, 9, 103sstr4g 3381 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549  wex 1550   wceq 1652  cab 2421   wss 3312  cop 3809  copab 4257 This theorem is referenced by:  ssopab2b  4473  ssopab2i  4474  ssopab2dv  4475 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-in 3319  df-ss 3326  df-opab 4259
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