Metamath Proof Explorer


Theorem rp-frege25

Description: Closed form for a1dd . Alternate route to Proposition 25 of Frege1879 p. 42. (Contributed by RP, 24-Dec-2019)

Ref Expression
Assertion rp-frege25 ( ( 𝜑 → ( 𝜓𝜒 ) ) → ( 𝜑 → ( 𝜓 → ( 𝜃𝜒 ) ) ) )

Proof

Step Hyp Ref Expression
1 rp-frege24 ( ( 𝜓𝜒 ) → ( 𝜓 → ( 𝜃𝜒 ) ) )
2 frege5 ( ( ( 𝜓𝜒 ) → ( 𝜓 → ( 𝜃𝜒 ) ) ) → ( ( 𝜑 → ( 𝜓𝜒 ) ) → ( 𝜑 → ( 𝜓 → ( 𝜃𝜒 ) ) ) ) )
3 1 2 ax-mp ( ( 𝜑 → ( 𝜓𝜒 ) ) → ( 𝜑 → ( 𝜓 → ( 𝜃𝜒 ) ) ) )