Theorem frege58acor 44416

Description: Lemma for frege59a 44417. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem frege58acor

Step	Hyp	Ref	Expression
1		ax-frege58a 44415	. 2 ⊢ (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → if-(𝜑, (𝜓 → 𝜒), (𝜃 → 𝜏)))
2		ifpimim 44049	. 2 ⊢ (if-(𝜑, (𝜓 → 𝜒), (𝜃 → 𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏)))
3	1, 2	syl 17	1 ⊢ (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏)))

Syntax hints:   → wi 4   ∧ wa 399  if-wif 1073

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege58a 44415

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-ifp 1074

This theorem is referenced by:  frege59a  44417  frege60a  44418  frege62a  44420