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Theorem orandc 923
 Description: Disjunction in terms of conjunction (De Morgan's law), for decidable propositions. Compare Theorem *4.57 of [WhiteheadRussell] p. 120. (Contributed by Jim Kingdon, 13-Dec-2021.)
Assertion
Ref Expression
orandc DECID DECID

Proof of Theorem orandc
StepHypRef Expression
1 pm4.56 769 . 2
2 dcn 827 . . . . 5 DECID DECID
32adantr 274 . . . 4 DECID DECID DECID
4 dcn 827 . . . . 5 DECID DECID
54adantl 275 . . . 4 DECID DECID DECID
6 dcan 918 . . . 4 DECID DECID DECID
73, 5, 6sylc 62 . . 3 DECID DECID DECID
8 dcor 919 . . . 4 DECID DECID DECID
98imp 123 . . 3 DECID DECID DECID
10 con2bidc 860 . . 3 DECID DECID
117, 9, 10sylc 62 . 2 DECID DECID
121, 11mpbii 147 1 DECID DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wb 104   wo 697  DECID wdc 819 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 603  ax-in2 604  ax-io 698 This theorem depends on definitions:  df-bi 116  df-stab 816  df-dc 820 This theorem is referenced by:  gcdaddm  11661
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