Theorem frege58acor

Description: Lemma for frege59a . (Contributed by RP, 17-Apr-2020) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege58acor	⊢ ( ( ( 𝜓 → 𝜒 ) ∧ ( 𝜃 → 𝜏 ) ) → ( if- ( 𝜑 , 𝜓 , 𝜃 ) → if- ( 𝜑 , 𝜒 , 𝜏 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-frege58a	⊢ ( ( ( 𝜓 → 𝜒 ) ∧ ( 𝜃 → 𝜏 ) ) → if- ( 𝜑 , ( 𝜓 → 𝜒 ) , ( 𝜃 → 𝜏 ) ) )
2		ifpimim	⊢ ( if- ( 𝜑 , ( 𝜓 → 𝜒 ) , ( 𝜃 → 𝜏 ) ) → ( if- ( 𝜑 , 𝜓 , 𝜃 ) → if- ( 𝜑 , 𝜒 , 𝜏 ) ) )
3	1 2	syl	⊢ ( ( ( 𝜓 → 𝜒 ) ∧ ( 𝜃 → 𝜏 ) ) → ( if- ( 𝜑 , 𝜓 , 𝜃 ) → if- ( 𝜑 , 𝜒 , 𝜏 ) ) )