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Theorem xorbi12i 1290
Description: Equality property for XOR. (Contributed by Mario Carneiro, 4-Sep-2016.)
Hypotheses
Ref Expression
xorbi12.1 (𝜑𝜓)
xorbi12.2 (𝜒𝜃)
Assertion
Ref Expression
xorbi12i ((𝜑𝜒) ↔ (𝜓𝜃))

Proof of Theorem xorbi12i
StepHypRef Expression
1 xorbi12.1 . . . 4 (𝜑𝜓)
21a1i 9 . . 3 (⊤ → (𝜑𝜓))
3 xorbi12.2 . . . 4 (𝜒𝜃)
43a1i 9 . . 3 (⊤ → (𝜒𝜃))
52, 4xorbi12d 1289 . 2 (⊤ → ((𝜑𝜒) ↔ (𝜓𝜃)))
65trud 1268 1 ((𝜑𝜒) ↔ (𝜓𝜃))
Colors of variables: wff set class
Syntax hints:  wb 102  wtru 1260  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-tru 1262  df-xor 1283
This theorem is referenced by: (None)
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