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Mirrors > Home > ILE Home > Th. List > pm2.54dc | Unicode version |
Description: Deriving disjunction from implication for a decidable proposition. Based on theorem *2.54 of [WhiteheadRussell] p. 107. The converse, pm2.53 641, holds whether the proposition is decidable or not. (Contributed by Jim Kingdon, 26-Mar-2018.) |
Ref | Expression |
---|---|
pm2.54dc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dcn 746 | . 2 DECID DECID | |
2 | notnotrdc 751 | . . . . 5 DECID | |
3 | orc 633 | . . . . 5 | |
4 | 2, 3 | syl6 29 | . . . 4 DECID |
5 | 4 | a1d 22 | . . 3 DECID DECID |
6 | olc 632 | . . . 4 | |
7 | 6 | a1i 9 | . . 3 DECID |
8 | 5, 7 | jaddc 761 | . 2 DECID DECID |
9 | 1, 8 | mpd 13 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wo 629 DECID wdc 742 |
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 630 |
This theorem depends on definitions: df-bi 110 df-dc 743 |
This theorem is referenced by: dfordc 791 pm2.68dc 793 pm4.79dc 809 pm5.11dc 815 |
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