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Mirrors > Home > ILE Home > Th. List > orbididc | Unicode version |
Description: Disjunction distributes over the biconditional, for a decidable proposition. Based on an axiom of system DS in Vladimir Lifschitz, "On calculational proofs" (1998), http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.3384. (Contributed by Jim Kingdon, 2-Apr-2018.) |
Ref | Expression |
---|---|
orbididc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orimdidc 812 | . . 3 DECID | |
2 | orimdidc 812 | . . 3 DECID | |
3 | 1, 2 | anbi12d 442 | . 2 DECID |
4 | dfbi2 368 | . . . 4 | |
5 | 4 | orbi2i 679 | . . 3 |
6 | ordi 729 | . . 3 | |
7 | 5, 6 | bitri 173 | . 2 |
8 | dfbi2 368 | . 2 | |
9 | 3, 7, 8 | 3bitr4g 212 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: 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-in2 545 ax-io 630 |
This theorem depends on definitions: df-bi 110 df-dc 743 |
This theorem is referenced by: pm5.7dc 861 |
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