Theorem jc 119

Description: Inference joining the consequents of two premises.

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		pm3.2im 107	. 2 ⊢ (ψ → (χ → ¬ (ψ → ¬ χ)))
2		jc.1	. 2 ⊢ (φ → ψ)
3		jc.2	. 2 ⊢ (φ → χ)
4	1, 2, 3	sylc 62	1 ⊢ (φ → ¬ (ψ → ¬ χ))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  bii 140  jca 236  msca 508

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

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