Theorem nsyl5 651

Description: A negated syllogism inference. (Contributed by Wolf Lammen, 20-May-2024.)

Hypotheses

Ref	Expression
nsyl4.1	⊢ (𝜑 → 𝜓)
nsyl4.2	⊢ (¬ 𝜑 → 𝜒)

Assertion

Ref	Expression
nsyl5	⊢ (¬ 𝜓 → 𝜒)

Proof of Theorem nsyl5

Step	Hyp	Ref	Expression
1		nsyl4.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	con3i 633	. 2 ⊢ (¬ 𝜓 → ¬ 𝜑)
3		nsyl4.2	. 2 ⊢ (¬ 𝜑 → 𝜒)
4	2, 3	syl 14	1 ⊢ (¬ 𝜓 → 𝜒)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 615  ax-in2 616

This theorem is referenced by: (None)