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Theorem truxorfal 1294
Description: A identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
truxorfal (( ⊤ ⊻ ⊥ ) ↔ ⊤ )

Proof of Theorem truxorfal
StepHypRef Expression
1 df-xor 1252 . 2 (( ⊤ ⊻ ⊥ ) ↔ (( ⊤ ⊥ ) ¬ ( ⊤ ⊥ )))
2 truorfal 1280 . . 3 (( ⊤ ⊥ ) ↔ ⊤ )
3 notfal 1288 . . . 4 (¬ ⊥ ↔ ⊤ )
4 truan 1245 . . . 4 (( ⊤ ⊥ ) ↔ ⊥ )
53, 4xchnxbir 593 . . 3 (¬ ( ⊤ ⊥ ) ↔ ⊤ )
62, 5anbi12i 436 . 2 ((( ⊤ ⊥ ) ¬ ( ⊤ ⊥ )) ↔ ( ⊤ ⊤ ))
7 anidm 376 . 2 (( ⊤ ⊤ ) ↔ ⊤ )
81, 6, 73bitri 195 1 (( ⊤ ⊻ ⊥ ) ↔ ⊤ )
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wa 97  wb 98   wo 616  wtru 1229  wfal 1233  wxo 1251
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 532  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-fal 1234  df-xor 1252
This theorem is referenced by: (None)
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