Theorem jc 139

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 137	. 2 ⊢ (ψ → (χ → ¬ (ψ → ¬ χ)))
4	1, 2, 3	sylc 56	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 is referenced by: (None)