Theorem jc 646

Description: Inference joining the consequents of two premises. (Contributed by NM, 5-Aug-1993.)

Hypotheses

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

Assertion

Ref	Expression
jc	⊢ (𝜑 → ¬ (𝜓 → ¬ 𝜒))

Proof of Theorem jc

Step	Hyp	Ref	Expression
1		jc.1	. 2 ⊢ (𝜑 → 𝜓)
2		jc.2	. 2 ⊢ (𝜑 → 𝜒)
3		pm3.2im 633	. 2 ⊢ (𝜓 → (𝜒 → ¬ (𝜓 → ¬ 𝜒)))
4	1, 2, 3	sylc 62	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-in1 610  ax-in2 611

This theorem is referenced by: (None)