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Mirrors > Home > ILE Home > Th. List > orandc | Unicode version |
Description: Disjunction in terms of conjunction (De Morgan's law), for decidable propositions. Compare Theorem *4.57 of [WhiteheadRussell] p. 120. (Contributed by Jim Kingdon, 13-Dec-2021.) |
Ref | Expression |
---|---|
orandc | DECID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.56 770 | . 2 | |
2 | dcn 828 | . . . . 5 DECID DECID | |
3 | 2 | adantr 274 | . . . 4 DECID DECID DECID |
4 | dcn 828 | . . . . 5 DECID DECID | |
5 | 4 | adantl 275 | . . . 4 DECID DECID DECID |
6 | dcan 919 | . . . 4 DECID DECID DECID | |
7 | 3, 5, 6 | sylc 62 | . . 3 DECID DECID DECID |
8 | dcor 920 | . . . 4 DECID DECID DECID | |
9 | 8 | imp 123 | . . 3 DECID DECID DECID |
10 | con2bidc 861 | . . 3 DECID DECID | |
11 | 7, 9, 10 | sylc 62 | . 2 DECID DECID |
12 | 1, 11 | mpbii 147 | 1 DECID 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-in1 604 ax-in2 605 ax-io 699 |
This theorem depends on definitions: df-bi 116 df-stab 817 df-dc 821 |
This theorem is referenced by: gcdaddm 11862 |
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