Theorem frege58acor 38170

Description: Lemma for frege59a 38171. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege58acor	|- ( ( ( ps -> ch ) /\ ( th -> ta ) ) -> (if- ( ph , ps , th ) -> if- ( ph , ch , ta ) ) )

Proof of Theorem frege58acor

Step	Hyp	Ref	Expression
1		ax-frege58a 38169	. 2 |- ( ( ( ps -> ch ) /\ ( th -> ta ) ) -> if- ( ph , ( ps -> ch ) , ( th -> ta ) ) )
2		ifpimim 37854	. 2 |- (if- ( ph , ( ps -> ch ) , ( th -> ta ) ) -> (if- ( ph , ps , th ) -> if- ( ph , ch , ta ) ) )
3	1, 2	syl 17	1 |- ( ( ( ps -> ch ) /\ ( th -> ta ) ) -> (if- ( ph , ps , th ) -> if- ( ph , ch , ta ) ) )

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

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege58a 38169

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ifp 1013

This theorem is referenced by:  frege59a  38171  frege60a  38172  frege62a  38174