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Mirrors > Home > ILE Home > Th. List > pm5.15dc | Unicode version |
Description: A decidable proposition is equivalent to a decidable proposition or its negation. Based on theorem *5.15 of [WhiteheadRussell] p. 124. (Contributed by Jim Kingdon, 18-Apr-2018.) |
Ref | Expression |
---|---|
pm5.15dc | DECID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xor3dc 1376 | . . . . 5 DECID DECID | |
2 | 1 | imp 123 | . . . 4 DECID DECID |
3 | 2 | biimpd 143 | . . 3 DECID DECID |
4 | dcbi 925 | . . . . 5 DECID DECID DECID | |
5 | 4 | imp 123 | . . . 4 DECID DECID DECID |
6 | dfordc 882 | . . . 4 DECID | |
7 | 5, 6 | syl 14 | . . 3 DECID DECID |
8 | 3, 7 | mpbird 166 | . 2 DECID DECID |
9 | 8 | ex 114 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 698 DECID wdc 824 |
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 821 df-dc 825 |
This theorem is referenced by: (None) |
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