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Mirrors > Home > ILE Home > Th. List > xordc | Unicode version |
Description: Two ways to express "exclusive or" between decidable propositions. Theorem *5.22 of [WhiteheadRussell] p. 124, but for decidable propositions. (Contributed by Jim Kingdon, 5-May-2018.) |
Ref | Expression |
---|---|
xordc | DECID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excxor 1341 | . . . 4 | |
2 | ancom 264 | . . . . 5 | |
3 | 2 | orbi2i 736 | . . . 4 |
4 | 1, 3 | bitri 183 | . . 3 |
5 | xornbidc 1354 | . . . 4 DECID DECID | |
6 | 5 | imp 123 | . . 3 DECID DECID |
7 | 4, 6 | syl5rbbr 194 | . 2 DECID DECID |
8 | 7 | ex 114 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 682 DECID wdc 804 wxo 1338 |
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 588 ax-in2 589 ax-io 683 |
This theorem depends on definitions: df-bi 116 df-stab 801 df-dc 805 df-xor 1339 |
This theorem is referenced by: dfbi3dc 1360 pm5.24dc 1361 |
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