Theorem frege61a

Description: Lemma for frege65a . Proposition 61 of Frege1879 p. 52. (Contributed by RP, 17-Apr-2020) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege61a	$$⊢\left(if-\left(\phi ,\psi ,\chi \right)\to \theta \right)\to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-frege58a	$$⊢\left(\psi \wedge \chi \right)\to if-\left(\phi ,\psi ,\chi \right)$$
2		frege9	$$⊢\left(\left(\psi \wedge \chi \right)\to if-\left(\phi ,\psi ,\chi \right)\right)\to \left(\left(if-\left(\phi ,\psi ,\chi \right)\to \theta \right)\to \left(\left(\psi \wedge \chi \right)\to \theta \right)\right)$$
3	1 2	ax-mp	$$⊢\left(if-\left(\phi ,\psi ,\chi \right)\to \theta \right)\to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$