Theorem wl-jarri 32467

Description: Dropping a nested antecedent. This theorem is one of two reversions of ja 172. Since ja 172 is reversible, a nested (chain of) implication(s) is just a packed notation of two or more theorems/hypotheses with a common consequent. axc5c7 33214 is an instance of this idea. (Contributed by Wolf Lammen, 20-Sep-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
wl-jarri.1	⊢ ((𝜑 → 𝜓) → 𝜒)

Assertion

Ref	Expression
wl-jarri	⊢ (𝜓 → 𝜒)

Proof of Theorem wl-jarri

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜓 → (𝜑 → 𝜓))
2		wl-jarri.1	. 2 ⊢ ((𝜑 → 𝜓) → 𝜒)
3	1, 2	syl 17	1 ⊢ (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: (None)