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Theorem ccased 913
 Description: Deduction for combining cases. (Contributed by NM, 9-May-2004.)
Hypotheses
Ref Expression
ccased.1 (φ → ((ψ χ) → η))
ccased.2 (φ → ((θ χ) → η))
ccased.3 (φ → ((ψ τ) → η))
ccased.4 (φ → ((θ τ) → η))
Assertion
Ref Expression
ccased (φ → (((ψ θ) (χ τ)) → η))

Proof of Theorem ccased
StepHypRef Expression
1 ccased.1 . . . 4 (φ → ((ψ χ) → η))
21com12 27 . . 3 ((ψ χ) → (φη))
3 ccased.2 . . . 4 (φ → ((θ χ) → η))
43com12 27 . . 3 ((θ χ) → (φη))
5 ccased.3 . . . 4 (φ → ((ψ τ) → η))
65com12 27 . . 3 ((ψ τ) → (φη))
7 ccased.4 . . . 4 (φ → ((θ τ) → η))
87com12 27 . . 3 ((θ τ) → (φη))
92, 4, 6, 8ccase 912 . 2 (((ψ θ) (χ τ)) → (φη))
109com12 27 1 (φ → (((ψ θ) (χ τ)) → η))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 357   ∧ wa 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360 This theorem is referenced by: (None)
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