Theorem unitreslOLD 874

Description: Obsolete version of olcnd 873 as of 13-Apr-2024. (Contributed by Giovanni Mascellani, 15-Sep-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
unitreslOLD	⊢ (𝜑 → 𝜓)

Proof of Theorem unitreslOLD

Step	Hyp	Ref	Expression
1		olcnd.1	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜒))
2		olcnd.2	. 2 ⊢ (𝜑 → ¬ 𝜒)
3		orcom 866	. . 3 ⊢ ((𝜓 ∨ 𝜒) ↔ (𝜒 ∨ 𝜓))
4		df-or 844	. . 3 ⊢ ((𝜒 ∨ 𝜓) ↔ (¬ 𝜒 → 𝜓))
5	3, 4	sylbb 221	. 2 ⊢ ((𝜓 ∨ 𝜒) → (¬ 𝜒 → 𝜓))
6	1, 2, 5	sylc 65	1 ⊢ (𝜑 → 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 843

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 209  df-or 844

This theorem is referenced by: (None)