Metamath Proof Explorer


Theorem rp-frege24

Description: Introducing an embedded antecedent. Alternate proof for frege24 . Closed form for a1d . (Contributed by RP, 24-Dec-2019)

Ref Expression
Assertion rp-frege24 ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) )

Proof

Step Hyp Ref Expression
1 rp-simp2-frege ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜓 ) ) )
2 ax-frege2 ⊢ ( ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) ) )
3 1 2 ax-mp ⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) )