Metamath Proof Explorer

Theorem wl-luk-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. Copy of pm2.04 with a different proof. (Contributed by Wolf Lammen, 7-Jul-2019) (New usage is discouraged.) (Proof modification is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		wl-luk-ax1	⊢ ( 𝜓 → ( 𝜑 → 𝜓 ) )
2		wl-luk-ax2	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) )
3	1 2	wl-luk-imtrid	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → ( 𝜑 → 𝜒 ) ) )