Theorem frege61a 38173

Description: Lemma for frege65a 38177. Proposition 61 of [Frege1879] p. 52. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege61a	|- ( (if- ( ph , ps , ch ) -> th ) -> ( ( ps /\ ch ) -> th ) )

Proof of Theorem frege61a

Step	Hyp	Ref	Expression
1		ax-frege58a 38169	. 2 |- ( ( ps /\ ch ) -> if- ( ph , ps , ch ) )
2		frege9 38106	. 2 |- ( ( ( ps /\ ch ) -> if- ( ph , ps , ch ) ) -> ( (if- ( ph , ps , ch ) -> th ) -> ( ( ps /\ ch ) -> th ) ) )
3	1, 2	ax-mp 5	1 |- ( (if- ( ph , ps , ch ) -> th ) -> ( ( ps /\ ch ) -> th ) )

Syntax hints:   -> wi 4   /\ wa 384  if-wif 1012

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085  ax-frege8 38103  ax-frege58a 38169

This theorem is referenced by:  frege65a  38177