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Theorem anxordi 1288
Description: Conjunction distributes over exclusive-or. (Contributed by Mario Carneiro and Jim Kingdon, 7-Oct-2018.)
Assertion
Ref Expression
anxordi  \/_  \/_

Proof of Theorem anxordi
StepHypRef Expression
1 simpl 102 . 2  \/_
2 df-xor 1266 . . . 4  \/_
32simplbi 259 . . 3  \/_
4 simpl 102 . . . 4
5 simpl 102 . . . 4
64, 5jaoi 635 . . 3
73, 6syl 14 . 2  \/_
8 ibar 285 . . 3  \/_  \/_
9 ibar 285 . . . 4
10 ibar 285 . . . 4
119, 10xorbi12d 1271 . . 3  \/_  \/_
128, 11bitr3d 179 . 2  \/_  \/_
131, 7, 12pm5.21nii 619 1  \/_  \/_
Colors of variables: wff set class
Syntax hints:   wn 3   wa 97   wb 98   wo 628    \/_ wxo 1265
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 629
This theorem depends on definitions:  df-bi 110  df-xor 1266
This theorem is referenced by:  rpnegap  8390
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