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Mirrors > Home > ILE Home > Th. List > xoranor | Unicode version |
Description: One way of defining exclusive or. Equivalent to df-xor 1307. (Contributed by Jim Kingdon and Mario Carneiro, 1-Mar-2018.) |
Ref | Expression |
---|---|
xoranor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor 1307 | . . 3 | |
2 | ax-ia3 106 | . . . . . . 7 | |
3 | 2 | con3d 593 | . . . . . 6 |
4 | olc 664 | . . . . . 6 | |
5 | 3, 4 | syl6 33 | . . . . 5 |
6 | pm3.21 260 | . . . . . . 7 | |
7 | 6 | con3d 593 | . . . . . 6 |
8 | orc 665 | . . . . . 6 | |
9 | 7, 8 | syl6 33 | . . . . 5 |
10 | 5, 9 | jaoi 668 | . . . 4 |
11 | 10 | imdistani 433 | . . 3 |
12 | 1, 11 | sylbi 119 | . 2 |
13 | pm3.14 702 | . . . 4 | |
14 | 13 | anim2i 334 | . . 3 |
15 | 14, 1 | sylibr 132 | . 2 |
16 | 12, 15 | impbii 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 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: excxor 1309 xoror 1310 |
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