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Mirrors > Home > ILE Home > Th. List > imordc | Unicode version |
Description: Implication in terms of disjunction for a decidable proposition. Based on theorem *4.6 of [WhiteheadRussell] p. 120. The reverse direction, imorr 830, holds for all propositions. (Contributed by Jim Kingdon, 20-Apr-2018.) |
Ref | Expression |
---|---|
imordc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnotbdc 799 | . . 3 DECID | |
2 | 1 | imbi1d 229 | . 2 DECID |
3 | dcn 779 | . . 3 DECID DECID | |
4 | dfordc 824 | . . 3 DECID | |
5 | 3, 4 | syl 14 | . 2 DECID |
6 | 2, 5 | bitr4d 189 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 103 wo 661 DECID wdc 775 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 |
This theorem depends on definitions: df-bi 115 df-dc 776 |
This theorem is referenced by: pm4.62dc 831 pm2.26dc 846 nf4dc 1600 algcvgblem 10431 divgcdodd 10522 |
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