ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  xorbi12i Unicode version

Theorem xorbi12i 1344
Description: Equality property for XOR. (Contributed by Mario Carneiro, 4-Sep-2016.)
Hypotheses
Ref Expression
xorbi12.1  |-  ( ph  <->  ps )
xorbi12.2  |-  ( ch  <->  th )
Assertion
Ref Expression
xorbi12i  |-  ( (
ph  \/_  ch )  <->  ( ps  \/_  th )
)

Proof of Theorem xorbi12i
StepHypRef Expression
1 xorbi12.1 . . . 4  |-  ( ph  <->  ps )
21a1i 9 . . 3  |-  ( T. 
->  ( ph  <->  ps )
)
3 xorbi12.2 . . . 4  |-  ( ch  <->  th )
43a1i 9 . . 3  |-  ( T. 
->  ( ch  <->  th )
)
52, 4xorbi12d 1343 . 2  |-  ( T. 
->  ( ( ph  \/_  ch ) 
<->  ( ps  \/_  th )
) )
65mptru 1323 1  |-  ( (
ph  \/_  ch )  <->  ( ps  \/_  th )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 104   T. wtru 1315    \/_ wxo 1336
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-xor 1337
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator