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Mirrors > Home > ILE Home > Th. List > anxordi | Unicode version |
Description: Conjunction distributes over exclusive-or. (Contributed by Mario Carneiro and Jim Kingdon, 7-Oct-2018.) |
Ref | Expression |
---|---|
anxordi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 107 | . 2 | |
2 | df-xor 1307 | . . . 4 | |
3 | 2 | simplbi 268 | . . 3 |
4 | simpl 107 | . . . 4 | |
5 | simpl 107 | . . . 4 | |
6 | 4, 5 | jaoi 668 | . . 3 |
7 | 3, 6 | syl 14 | . 2 |
8 | ibar 295 | . . 3 | |
9 | ibar 295 | . . . 4 | |
10 | ibar 295 | . . . 4 | |
11 | 9, 10 | xorbi12d 1313 | . . 3 |
12 | 8, 11 | bitr3d 188 | . 2 |
13 | 1, 7, 12 | pm5.21nii 652 | 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: rpnegap 8766 |
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