Theorem frege63a

Description: Proposition 63 of Frege1879 p. 52. (Contributed by RP, 17-Apr-2020) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege63a	⊢ ( if- ( 𝜑 , 𝜓 , 𝜃 ) → ( 𝜂 → ( ( ( 𝜓 → 𝜒 ) ∧ ( 𝜃 → 𝜏 ) ) → if- ( 𝜑 , 𝜒 , 𝜏 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		frege62a	⊢ ( if- ( 𝜑 , 𝜓 , 𝜃 ) → ( ( ( 𝜓 → 𝜒 ) ∧ ( 𝜃 → 𝜏 ) ) → if- ( 𝜑 , 𝜒 , 𝜏 ) ) )
2		frege24	⊢ ( ( if- ( 𝜑 , 𝜓 , 𝜃 ) → ( ( ( 𝜓 → 𝜒 ) ∧ ( 𝜃 → 𝜏 ) ) → if- ( 𝜑 , 𝜒 , 𝜏 ) ) ) → ( if- ( 𝜑 , 𝜓 , 𝜃 ) → ( 𝜂 → ( ( ( 𝜓 → 𝜒 ) ∧ ( 𝜃 → 𝜏 ) ) → if- ( 𝜑 , 𝜒 , 𝜏 ) ) ) ) )
3	1 2	ax-mp	⊢ ( if- ( 𝜑 , 𝜓 , 𝜃 ) → ( 𝜂 → ( ( ( 𝜓 → 𝜒 ) ∧ ( 𝜃 → 𝜏 ) ) → if- ( 𝜑 , 𝜒 , 𝜏 ) ) ) )