Theorem jarl 584

Description: Elimination of a nested antecedent. (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		pm2.21 547	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2	1	imim1i 54	1 ⊢ (((𝜑 → 𝜓) → 𝜒) → (¬ 𝜑 → 𝜒))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in2 545

This theorem is referenced by:  pm2.68dc  793