Theorem nsyl2OLD 152

Description: Obsolete version of nsyl2 143 as of 14-Nov-2023. (Contributed by NM, 26-Jun-1994.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nsyl2OLD.1	⊢ (𝜑 → ¬ 𝜓)
nsyl2OLD.2	⊢ (¬ 𝜒 → 𝜓)

Assertion

Ref	Expression
nsyl2OLD	⊢ (𝜑 → 𝜒)

Proof of Theorem nsyl2OLD

Step	Hyp	Ref	Expression
1		nsyl2OLD.1	. 2 ⊢ (𝜑 → ¬ 𝜓)
2		nsyl2OLD.2	. . 3 ⊢ (¬ 𝜒 → 𝜓)
3	2	a1i 11	. 2 ⊢ (𝜑 → (¬ 𝜒 → 𝜓))
4	1, 3	mt3d 150	1 ⊢ (𝜑 → 𝜒)

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)