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

Theorem xoranor 1284
 Description: One way of defining exclusive or. Equivalent to df-xor 1283. (Contributed by Jim Kingdon and Mario Carneiro, 1-Mar-2018.)
Assertion
Ref Expression
xoranor

Proof of Theorem xoranor
StepHypRef Expression
1 df-xor 1283 . . 3
2 ax-ia3 105 . . . . . . 7
32con3d 571 . . . . . 6
4 olc 642 . . . . . 6
53, 4syl6 33 . . . . 5
6 pm3.21 255 . . . . . . 7
76con3d 571 . . . . . 6
8 orc 643 . . . . . 6
97, 8syl6 33 . . . . 5
105, 9jaoi 646 . . . 4
1110imdistani 427 . . 3
121, 11sylbi 118 . 2
13 pm3.14 680 . . . 4
1413anim2i 328 . . 3
1514, 1sylibr 141 . 2
1612, 15impbii 121 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 101   wb 102   wo 639   wxo 1282 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640 This theorem depends on definitions:  df-bi 114  df-xor 1283 This theorem is referenced by:  excxor  1285  xoror  1286
 Copyright terms: Public domain W3C validator