ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  xoranor Structured version   Unicode version

Theorem xoranor 1267
Description: One way of defining exclusive or. Equivalent to df-xor 1266. (Contributed by Jim Kingdon and Mario Carneiro, 1-Mar-2018.)
Assertion
Ref Expression
xoranor  \/_

Proof of Theorem xoranor
StepHypRef Expression
1 df-xor 1266 . . 3  \/_
2 ax-ia3 101 . . . . . . 7
32con3d 560 . . . . . 6
4 olc 631 . . . . . 6
53, 4syl6 29 . . . . 5
6 pm3.21 251 . . . . . . 7
76con3d 560 . . . . . 6
8 orc 632 . . . . . 6
97, 8syl6 29 . . . . 5
105, 9jaoi 635 . . . 4
1110imdistani 419 . . 3
121, 11sylbi 114 . 2  \/_
13 pm3.14 669 . . . 4
1413anim2i 324 . . 3
1514, 1sylibr 137 . 2  \/_
1612, 15impbii 117 1  \/_
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   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:  excxor  1268
  Copyright terms: Public domain W3C validator