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Theorem xordc 1280
Description: Two ways to express "exclusive or" between decidable propositions. Theorem *5.22 of [WhiteheadRussell] p. 124, but for decidable propositions. (Contributed by Jim Kingdon, 5-May-2018.)
Assertion
Ref Expression
xordc DECID DECID

Proof of Theorem xordc
StepHypRef Expression
1 excxor 1268 . . . 4  \/_
2 ancom 253 . . . . 5
32orbi2i 678 . . . 4
41, 3bitri 173 . . 3  \/_
5 xornbidc 1279 . . . 4 DECID DECID  \/_
65imp 115 . . 3 DECID DECID  \/_
74, 6syl5rbbr 184 . 2 DECID DECID
87ex 108 1 DECID DECID
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wb 98   wo 628  DECID wdc 741    \/_ 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-dc 742  df-xor 1266
This theorem is referenced by:  dfbi3dc  1285  pm5.24dc  1286
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