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Mirrors > Home > ILE Home > Th. List > xor3dc | Unicode version |
Description: Two ways to express "exclusive or" between decidable propositions. (Contributed by Jim Kingdon, 12-Apr-2018.) |
Ref | Expression |
---|---|
xor3dc | DECID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dcn 746 | . . . . . 6 DECID DECID | |
2 | dcbi 844 | . . . . . 6 DECID DECID DECID | |
3 | 1, 2 | syl5 28 | . . . . 5 DECID DECID DECID |
4 | 3 | imp 115 | . . . 4 DECID DECID DECID |
5 | pm5.18dc 777 | . . . . . . 7 DECID DECID | |
6 | 5 | imp 115 | . . . . . 6 DECID DECID |
7 | 6 | a1d 22 | . . . . 5 DECID DECID DECID |
8 | 7 | con2biddc 774 | . . . 4 DECID DECID DECID |
9 | 4, 8 | mpd 13 | . . 3 DECID DECID |
10 | 9 | bicomd 129 | . 2 DECID DECID |
11 | 10 | ex 108 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 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: pm5.15dc 1280 xor2dc 1281 nbbndc 1285 |
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