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Mirrors > Home > ILE Home > Th. List > testbitestn | Unicode version |
Description: A proposition is testable iff its negation is testable. See also dcn 779 (which could be read as "Decidability implies testability"). (Contributed by David A. Wheeler, 6-Dec-2018.) |
Ref | Expression |
---|---|
testbitestn | DECID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnotnot 660 | . . . 4 | |
2 | 1 | orbi2i 711 | . . 3 |
3 | orcom 679 | . . 3 | |
4 | 2, 3 | bitri 182 | . 2 |
5 | df-dc 776 | . 2 DECID | |
6 | df-dc 776 | . 2 DECID | |
7 | 4, 5, 6 | 3bitr4ri 211 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wb 103 wo 661 DECID wdc 775 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 |
This theorem depends on definitions: df-bi 115 df-dc 776 |
This theorem is referenced by: (None) |
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