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Theorem pm4.54dc 804
Description: Theorem *4.54 of [WhiteheadRussell] p. 120, for decidable propositions. One form of DeMorgan's law. (Contributed by Jim Kingdon, 2-May-2018.)
Assertion
Ref Expression
pm4.54dc DECID DECID

Proof of Theorem pm4.54dc
StepHypRef Expression
1 dcn 745 . . . . 5 DECID DECID
2 dfandc 777 . . . . 5 DECID DECID
31, 2syl 14 . . . 4 DECID DECID
43imp 115 . . 3 DECID DECID
5 pm4.66dc 801 . . . . 5 DECID
65adantr 261 . . . 4 DECID DECID
76notbid 591 . . 3 DECID DECID
84, 7bitrd 177 . 2 DECID DECID
98ex 108 1 DECID DECID
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wb 98   wo 628  DECID wdc 741
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by:  pm4.55dc  845
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