Metamath Proof Explorer

Theorem frege5

Description: A closed form of syl . Identical to imim2 . Theorem *2.05 of WhiteheadRussell p. 100. Proposition 5 of Frege1879 p. 32. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	frege5	$⊢ (φ \to ψ) \to ((χ \to φ) \to (χ \to ψ))$

Proof

Step	Hyp	Ref	Expression
1		ax-frege1	$⊢ (φ \to ψ) \to (χ \to (φ \to ψ))$
2		frege4	$⊢ ((φ \to ψ) \to (χ \to (φ \to ψ))) \to ((φ \to ψ) \to ((χ \to φ) \to (χ \to ψ)))$
3	1 2	ax-mp	$⊢ (φ \to ψ) \to ((χ \to φ) \to (χ \to ψ))$