Theorem jarl 155

Description: Elimination of a nested antecedent as a kind of reversal of inference ja 153. (Contributed by Wolf Lammen, 10-May-2013.)

Assertion

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

Proof of Theorem jarl

Step	Hyp	Ref	Expression
1		pm2.21 100	. 2 ⊢ (¬ φ → (φ → ψ))
2	1	imim1i 54	1 ⊢ (((φ → ψ) → χ) → (¬ φ → χ))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  pm2.68  399  merco2  1501