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Theorem pm5.18dc 869
 Description: Relationship between an equivalence and an equivalence with some negation, for decidable propositions. Based on theorem *5.18 of [WhiteheadRussell] p. 124. Given decidability, we can consider to represent "negated exclusive-or". (Contributed by Jim Kingdon, 4-Apr-2018.)
Assertion
Ref Expression
pm5.18dc DECID DECID

Proof of Theorem pm5.18dc
StepHypRef Expression
1 df-dc 821 . 2 DECID
2 pm5.501 243 . . . . . . . 8
32a1d 22 . . . . . . 7 DECID
43con1biddc 862 . . . . . 6 DECID
54imp 123 . . . . 5 DECID
6 pm5.501 243 . . . . . 6
76adantr 274 . . . . 5 DECID
85, 7bitr2d 188 . . . 4 DECID
98ex 114 . . 3 DECID
10 dcn 828 . . . . . . 7 DECID DECID
11 nbn2 687 . . . . . . . . 9
1211a1d 22 . . . . . . . 8 DECID
1312con1biddc 862 . . . . . . 7 DECID
1410, 13syl5 32 . . . . . 6 DECID
1514imp 123 . . . . 5 DECID
16 nbn2 687 . . . . . 6
1716adantr 274 . . . . 5 DECID
1815, 17bitr2d 188 . . . 4 DECID
1918ex 114 . . 3 DECID
209, 19jaoi 706 . 2 DECID
211, 20sylbi 120 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 This theorem is referenced by:  xor3dc  1366  dfbi3dc  1376
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