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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, pm2.53 722, holds whether the proposition is decidable or not. (Contributed by Jim Kingdon, 26-Mar-2018.) |
Ref | Expression |
---|---|
pm2.54dc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dcn 842 |
. 2
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2 | notnotrdc 843 |
. . . . 5
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3 | orc 712 |
. . . . 5
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4 | 2, 3 | syl6 33 |
. . . 4
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5 | 4 | a1d 22 |
. . 3
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6 | olc 711 |
. . . 4
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7 | 6 | a1i 9 |
. . 3
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8 | 5, 7 | jaddc 864 |
. 2
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9 | 1, 8 | mpd 13 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 |
This theorem depends on definitions: df-bi 117 df-dc 835 |
This theorem is referenced by: dfordc 892 pm2.68dc 894 pm4.79dc 903 pm5.11dc 909 |
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