Metamath Proof Explorer

Theorem pm2.04

Description: Swap antecedents. Theorem *2.04 of WhiteheadRussell p. 100. This was the third axiom in Frege's logic system, specifically Proposition 8 of Frege1879 p. 35. Its associated inference is com12 . (Contributed by NM, 27-Dec-1992) (Proof shortened by Wolf Lammen, 12-Sep-2012)

		Ref	Expression
	Assertion	pm2.04	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → ( 𝜑 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → 𝜒 ) ) )
2	1	com23	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → ( 𝜑 → 𝜒 ) ) )