Theorem rp-7frege

Description: Distribute antecedent and add another. (Contributed by RP, 24-Dec-2019)

	Ref	Expression
Assertion	rp-7frege	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜃 → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-frege2	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) )
2		rp-frege24	⊢ ( ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) ) → ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜃 → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜃 → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) ) )