Theorem jarr 107

Description: Elimination of a nested antecedent. Sometimes called "Syll-Simp" since it is a syllogism applied to ax-1 6 ("Simplification"). (Contributed by Wolf Lammen, 9-May-2013.)

Assertion

Ref	Expression
jarr	⊢ (((𝜑 → 𝜓) → 𝜒) → (𝜓 → 𝜒))

Proof of Theorem jarr

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜓 → (𝜑 → 𝜓))
2	1	imim1i 64	1 ⊢ (((𝜑 → 𝜓) → 𝜒) → (𝜓 → 𝜒))

This proof depends on syntax axioms:   → wi 4

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

This theorem is used by:  loolin  112  loowoz  113  minimp  1654  bj-stabpeirce  37391  bj-sbievw2  37728  ax3h  47907  adh-jarrsc  48014  adh-minimp  48027