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Mirrors > Home > ILE Home > Th. List > pm5.17dc | Unicode version |
Description: Two ways of stating exclusive-or which are equivalent for a decidable proposition. Based on theorem *5.17 of [WhiteheadRussell] p. 124. (Contributed by Jim Kingdon, 16-Apr-2018.) |
Ref | Expression |
---|---|
pm5.17dc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bicom 138 | . 2 | |
2 | dfbi2 380 | . . 3 | |
3 | orcom 679 | . . . . 5 | |
4 | dfordc 824 | . . . . 5 DECID | |
5 | 3, 4 | syl5rbb 191 | . . . 4 DECID |
6 | imnan 656 | . . . . 5 | |
7 | 6 | a1i 9 | . . . 4 DECID |
8 | 5, 7 | anbi12d 456 | . . 3 DECID |
9 | 2, 8 | syl5bb 190 | . 2 DECID |
10 | 1, 9 | syl5rbb 191 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 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: xor2dc 1321 |
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