Theorem ecase 908

Description: Inference for elimination by cases. (Contributed by NM, 13-Jul-2005.)

Hypotheses

Ref	Expression
ecase.1	⊢ (¬ φ → χ)
ecase.2	⊢ (¬ ψ → χ)
ecase.3	⊢ ((φ ∧ ψ) → χ)

Assertion

Ref	Expression
ecase	⊢ χ

Proof of Theorem ecase

Step	Hyp	Ref	Expression
1		ecase.3	. . 3 ⊢ ((φ ∧ ψ) → χ)
2	1	ex 423	. 2 ⊢ (φ → (ψ → χ))
3		ecase.1	. 2 ⊢ (¬ φ → χ)
4		ecase.2	. 2 ⊢ (¬ ψ → χ)
5	2, 3, 4	pm2.61nii 158	1 ⊢ χ

Syntax hints:  ¬ wn 3   → wi 4   ∧ 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-an 360

This theorem is referenced by: (None)