Theorem ecase3 1029

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 854	. 2 ⊢ ((𝜑 ∨ 𝜓) → 𝜒)
4		ecase3.3	. 2 ⊢ (¬ (𝜑 ∨ 𝜓) → 𝜒)
5	3, 4	pm2.61i 182	1 ⊢ 𝜒

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 844

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 206  df-or 845

This theorem is referenced by:  eueq3  3646  lcmfunsnlem2  16345