Theorem jarr 106

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 63	1 ⊢ (((𝜑 → 𝜓) → 𝜒) → (𝜓 → 𝜒))

Syntax hints:   → wi 4

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

This theorem is referenced by:  loolin  111  loowoz  112  minimp  1622  bj-stabpeirce  33896  bj-sbievw2  34177  ax3h  43219  adh-jarrsc  43326  adh-minimp  43339