Theorem ecase3 907

Description: Inference for elimination by cases. (Contributed by NM, 23-Mar-1995.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)

Hypotheses

Ref	Expression
ecase3.1	⊢ (φ → χ)
ecase3.2	⊢ (ψ → χ)
ecase3.3	⊢ (¬ (φ ∨ ψ) → χ)

Assertion

Ref	Expression
ecase3	⊢ χ

Proof of Theorem ecase3

Step	Hyp	Ref	Expression
1		ecase3.1	. . 3 ⊢ (φ → χ)
2		ecase3.2	. . 3 ⊢ (ψ → χ)
3	1, 2	jaoi 368	. 2 ⊢ ((φ ∨ ψ) → χ)
4		ecase3.3	. 2 ⊢ (¬ (φ ∨ ψ) → χ)
5	3, 4	pm2.61i 156	1 ⊢ χ

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357

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

This theorem is referenced by:  equvini  1987  eueq3  3012