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Mirrors > Home > ILE Home > Th. List > anordc | Unicode version |
Description: Conjunction in terms of disjunction (DeMorgan's law). Theorem *4.5 of [WhiteheadRussell] p. 120, but where the propositions are decidable. The forward direction, pm3.1 670, holds for all propositions, but the equivalence only holds given decidability. (Contributed by Jim Kingdon, 21-Apr-2018.) |
Ref | Expression |
---|---|
anordc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dcan 841 |
. 2
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2 | ianordc 798 |
. . . . 5
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3 | 2 | bicomd 129 |
. . . 4
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4 | 3 | a1d 22 |
. . 3
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5 | 4 | con2biddc 773 |
. 2
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6 | 1, 5 | syld 40 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
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 629 |
This theorem depends on definitions: df-bi 110 df-dc 742 |
This theorem is referenced by: pm3.11dc 863 dn1dc 866 |
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