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Theorem xorbi12i 1314
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)
2 xorbi12.2 . . . 4 (χθ)
31, 2bibi12i 306 . . 3 ((φχ) ↔ (ψθ))
43notbii 287 . 2 (¬ (φχ) ↔ ¬ (ψθ))
5 df-xor 1305 . 2 ((φχ) ↔ ¬ (φχ))
6 df-xor 1305 . 2 ((ψθ) ↔ ¬ (ψθ))
74, 5, 63bitr4i 268 1 ((φχ) ↔ (ψθ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176  wxo 1304
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-xor 1305
This theorem is referenced by:  hadcoma  1388  hadcomb  1389  hadnot  1393
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