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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 1269 | . . . 4 | |
2 | ancom 253 | . . . . 5 | |
3 | 2 | orbi2i 679 | . . . 4 |
4 | 1, 3 | bitri 173 | . . 3 |
5 | xornbidc 1282 | . . . 4 DECID DECID | |
6 | 5 | imp 115 | . . 3 DECID DECID |
7 | 4, 6 | syl5rbbr 184 | . 2 DECID DECID |
8 | 7 | ex 108 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 wo 629 DECID wdc 742 wxo 1266 |
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 df-xor 1267 |
This theorem is referenced by: dfbi3dc 1288 pm5.24dc 1289 |
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