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Mirrors > Home > ILE Home > Th. List > pm4.83dc | Unicode version |
Description: Theorem *4.83 of [WhiteheadRussell] p. 122, for decidable propositions. As with other case elimination theorems, like pm2.61dc 851, it only holds for decidable propositions. (Contributed by Jim Kingdon, 12-May-2018.) |
Ref | Expression |
---|---|
pm4.83dc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dc 821 | . . 3 DECID | |
2 | pm3.44 705 | . . . 4 | |
3 | 2 | com12 30 | . . 3 |
4 | 1, 3 | sylbi 120 | . 2 DECID |
5 | ax-1 6 | . . 3 | |
6 | ax-1 6 | . . 3 | |
7 | 5, 6 | jca 304 | . 2 |
8 | 4, 7 | impbid1 141 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 698 DECID wdc 820 |
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-io 699 |
This theorem depends on definitions: df-bi 116 df-dc 821 |
This theorem is referenced by: (None) |
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