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Mirrors > Home > ILE Home > Th. List > excxor | Unicode version |
Description: This tautology shows that xor is really exclusive. (Contributed by FL, 22-Nov-2010.) (Proof rewritten by Jim Kingdon, 5-May-2018.) |
Ref | Expression |
---|---|
excxor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xoranor 1308 | . . 3 | |
2 | andi 764 | . . 3 | |
3 | orcom 679 | . . . . 5 | |
4 | pm3.24 659 | . . . . . 6 | |
5 | 4 | biorfi 697 | . . . . 5 |
6 | andir 765 | . . . . 5 | |
7 | 3, 5, 6 | 3bitr4ri 211 | . . . 4 |
8 | pm5.61 740 | . . . 4 | |
9 | 7, 8 | orbi12i 713 | . . 3 |
10 | 1, 2, 9 | 3bitri 204 | . 2 |
11 | orcom 679 | . 2 | |
12 | ancom 262 | . . 3 | |
13 | 12 | orbi2i 711 | . 2 |
14 | 10, 11, 13 | 3bitri 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 102 wb 103 wo 661 wxo 1306 |
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-xor 1307 |
This theorem is referenced by: xordc 1323 symdifxor 3230 |
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