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Theorem dfbi3dc 1376
 Description: An alternate definition of the biconditional for decidable propositions. Theorem *5.23 of [WhiteheadRussell] p. 124, but with decidability conditions. (Contributed by Jim Kingdon, 5-May-2018.)
Assertion
Ref Expression
dfbi3dc DECID DECID

Proof of Theorem dfbi3dc
StepHypRef Expression
1 dcn 828 . . . 4 DECID DECID
2 xordc 1371 . . . . 5 DECID DECID
32imp 123 . . . 4 DECID DECID
41, 3sylan2 284 . . 3 DECID DECID
5 pm5.18dc 869 . . . 4 DECID DECID
65imp 123 . . 3 DECID DECID
7 notnotbdc 858 . . . . . 6 DECID
87anbi2d 460 . . . . 5 DECID
9 ancom 264 . . . . . 6
109a1i 9 . . . . 5 DECID
118, 10orbi12d 783 . . . 4 DECID
1211adantl 275 . . 3 DECID DECID
134, 6, 123bitr4d 219 . 2 DECID DECID
1413ex 114 1 DECID DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wb 104   wo 698  DECID wdc 820 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699 This theorem depends on definitions:  df-bi 116  df-stab 817  df-dc 821  df-xor 1355 This theorem is referenced by:  pm5.24dc  1377
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