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Mirrors > Home > ILE Home > Th. List > ianordc | Unicode version |
Description: Negated conjunction in terms of disjunction (DeMorgan's law). Theorem *4.51 of [WhiteheadRussell] p. 120, but where one proposition is decidable. The reverse direction, pm3.14 670, holds for all propositions, but the equivalence only holds where one proposition is decidable. (Contributed by Jim Kingdon, 21-Apr-2018.) |
Ref | Expression |
---|---|
ianordc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imnan 624 | . 2 | |
2 | pm4.62dc 798 | . 2 DECID | |
3 | 1, 2 | syl5bbr 183 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 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: anordc 863 19.33bdc 1521 nn0n0n1ge2b 8320 |
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