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Metamath Proof Explorer

Theorem ccase2

Description: Inference for combining cases. (Contributed by NM, 29-Jul-1999)

Ref Expression
Hypotheses ccase2.1 ⊢ φ ∧ ψ → τ
ccase2.2 ⊢ χ → τ
ccase2.3 ⊢ θ → τ
Assertion ccase2 ⊢ φ ∨ χ ∧ ψ ∨ θ → τ

Proof

Step Hyp Ref Expression
1 ccase2.1 ⊢ φ ∧ ψ → τ
2 ccase2.2 ⊢ χ → τ
3 ccase2.3 ⊢ θ → τ
4 2 adantr ⊢ χ ∧ ψ → τ
5 3 adantl ⊢ φ ∧ θ → τ
6 3 adantl ⊢ χ ∧ θ → τ
7 1 4 5 6 ccase ⊢ φ ∨ χ ∧ ψ ∨ θ → τ