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Theorem ccase 912
 Description: Inference for combining cases. (Contributed by NM, 29-Jul-1999.) (Proof shortened by Wolf Lammen, 6-Jan-2013.)
Hypotheses
Ref Expression
ccase.1 ((φ ψ) → τ)
ccase.2 ((χ ψ) → τ)
ccase.3 ((φ θ) → τ)
ccase.4 ((χ θ) → τ)
Assertion
Ref Expression
ccase (((φ χ) (ψ θ)) → τ)

Proof of Theorem ccase
StepHypRef Expression
1 ccase.1 . . 3 ((φ ψ) → τ)
2 ccase.2 . . 3 ((χ ψ) → τ)
31, 2jaoian 759 . 2 (((φ χ) ψ) → τ)
4 ccase.3 . . 3 ((φ θ) → τ)
5 ccase.4 . . 3 ((χ θ) → τ)
64, 5jaoian 759 . 2 (((φ χ) θ) → τ)
73, 6jaodan 760 1 (((φ χ) (ψ θ)) → τ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 357   ∧ wa 358 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-or 359  df-an 360 This theorem is referenced by:  ccased  913  ccase2  914  undif3  3515
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