Theorem pm2.61iOLD 190

Description: Obsolete version of pm2.61i 184 as of 19-Nov-2023. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 12-Sep-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
pm2.61iOLD.1	⊢ (𝜑 → 𝜓)
pm2.61iOLD.2	⊢ (¬ 𝜑 → 𝜓)

Assertion

Ref	Expression
pm2.61iOLD	⊢ 𝜓

Proof of Theorem pm2.61iOLD

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝜑 → 𝜑)
2		pm2.61iOLD.2	. . 3 ⊢ (¬ 𝜑 → 𝜓)
3		pm2.61iOLD.1	. . 3 ⊢ (𝜑 → 𝜓)
4	2, 3	ja 188	. 2 ⊢ ((𝜑 → 𝜑) → 𝜓)
5	1, 4	ax-mp 5	1 ⊢ 𝜓

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by: (None)