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Theorem ssoprab2 6366
 Description: Equivalence of ordered pair abstraction subclass and implication. Compare ssopab2 4727. (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 22 . . . . . . 7
21anim2d 575 . . . . . 6
32aleximi 1712 . . . . 5
43aleximi 1712 . . . 4
54aleximi 1712 . . 3
65ss2abdv 3488 . 2
7 df-oprab 6312 . 2
8 df-oprab 6312 . 2
96, 7, 83sstr4g 3459 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376  wal 1450   wceq 1452  wex 1671  cab 2457   wss 3390  cop 3965  coprab 6309 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-in 3397  df-ss 3404  df-oprab 6312 This theorem is referenced by:  ssoprab2b  6367  joinfval  16325  meetfval  16339
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