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Theorem xorbi12d 1273
Description: Deduction joining two equivalences to form equivalence of exclusive-or. (Contributed by Jim Kingdon, 7-Oct-2018.)
Hypotheses
Ref Expression
xorbi12d.1 (φ → (ψχ))
xorbi12d.2 (φ → (θτ))
Assertion
Ref Expression
xorbi12d (φ → ((ψθ) ↔ (χτ)))

Proof of Theorem xorbi12d
StepHypRef Expression
1 xorbi12d.1 . . 3 (φ → (ψχ))
21xorbi1d 1272 . 2 (φ → ((ψθ) ↔ (χθ)))
3 xorbi12d.2 . . 3 (φ → (θτ))
43xorbi2d 1271 . 2 (φ → ((χθ) ↔ (χτ)))
52, 4bitrd 177 1 (φ → ((ψθ) ↔ (χτ)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wxo 1266
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 630
This theorem depends on definitions:  df-bi 110  df-xor 1267
This theorem is referenced by:  xorbi12i  1274  anxordi  1291  rpnegap  8482
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