Theorem unitreslOLD

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

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

Proof

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