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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 1366 | . . 3 | |
2 | andi 808 | . . 3 | |
3 | orcom 718 | . . . . 5 | |
4 | pm3.24 683 | . . . . . 6 | |
5 | 4 | biorfi 736 | . . . . 5 |
6 | andir 809 | . . . . 5 | |
7 | 3, 5, 6 | 3bitr4ri 212 | . . . 4 |
8 | pm5.61 784 | . . . 4 | |
9 | 7, 8 | orbi12i 754 | . . 3 |
10 | 1, 2, 9 | 3bitri 205 | . 2 |
11 | orcom 718 | . 2 | |
12 | ancom 264 | . . 3 | |
13 | 12 | orbi2i 752 | . 2 |
14 | 10, 11, 13 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wb 104 wo 698 wxo 1364 |
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 604 ax-in2 605 ax-io 699 |
This theorem depends on definitions: df-bi 116 df-xor 1365 |
This theorem is referenced by: xordc 1381 symdifxor 3384 |
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