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Theorem bijadc 775
Description: Combine antecedents into a single biconditional. This inference is reminiscent of jadc 759. (Contributed by Jim Kingdon, 4-May-2018.)
Hypotheses
Ref Expression
bijadc.1 (φ → (ψχ))
bijadc.2 φ → (¬ ψχ))
Assertion
Ref Expression
bijadc (DECID ψ → ((φψ) → χ))

Proof of Theorem bijadc
StepHypRef Expression
1 bi2 121 . . 3 ((φψ) → (ψφ))
2 bijadc.1 . . 3 (φ → (ψχ))
31, 2syli 33 . 2 ((φψ) → (ψχ))
4 bi1 111 . . . 4 ((φψ) → (φψ))
54con3d 560 . . 3 ((φψ) → (¬ ψ → ¬ φ))
6 bijadc.2 . . 3 φ → (¬ ψχ))
75, 6syli 33 . 2 ((φψ) → (¬ ψχ))
83, 7pm2.61ddc 757 1 (DECID ψ → ((φψ) → χ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98  DECID wdc 741
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 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by: (None)
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