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Mirrors > Home > ILE Home > Th. List > pm2.13dc | Unicode version |
Description: A decidable proposition or its triple negation is true. Theorem *2.13 of [WhiteheadRussell] p. 101 with decidability condition added. (Contributed by Jim Kingdon, 13-May-2018.) |
Ref | Expression |
---|---|
pm2.13dc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dc 776 | . . 3 DECID | |
2 | notnotrdc 784 | . . . . 5 DECID | |
3 | 2 | con3d 593 | . . . 4 DECID |
4 | 3 | orim2d 734 | . . 3 DECID |
5 | 1, 4 | syl5bi 150 | . 2 DECID DECID |
6 | 5 | pm2.43i 48 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 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: (None) |
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