Theorem jcndOLD 339

Description: Obsolete version of jcnd 165 as of 10-Apr-2024. (Contributed by Glauco Siliprandi, 11-Dec-2019.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
jcndOLD	⊢ (𝜑 → ¬ (𝜓 → 𝜒))

Proof of Theorem jcndOLD

Step	Hyp	Ref	Expression
1		jcndOLD.1	. . 3 ⊢ (𝜑 → 𝜓)
2		jcndOLD.2	. . 3 ⊢ (𝜑 → ¬ 𝜒)
3	1, 2	jc 163	. 2 ⊢ (𝜑 → ¬ (𝜓 → ¬ ¬ 𝜒))
4		notnotb 317	. . 3 ⊢ (𝜒 ↔ ¬ ¬ 𝜒)
5	4	imbi2i 338	. 2 ⊢ ((𝜓 → 𝜒) ↔ (𝜓 → ¬ ¬ 𝜒))
6	3, 5	sylnibr 331	1 ⊢ (𝜑 → ¬ (𝜓 → 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 depends on definitions:  df-bi 209

This theorem is referenced by: (None)