Theorem frege62a 38174

Description: A kind of Aristotelian inference. This judgement replaces the mode of inference barbara 2563 when the minor premise has a particular context. Proposition 62 of [Frege1879] p. 52. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege62a	|- (if- ( ph , ps , th ) -> ( ( ( ps -> ch ) /\ ( th -> ta ) ) -> if- ( ph , ch , ta ) ) )

Proof of Theorem frege62a

Step	Hyp	Ref	Expression
1		frege58acor 38170	. 2 |- ( ( ( ps -> ch ) /\ ( th -> ta ) ) -> (if- ( ph , ps , th ) -> if- ( ph , ch , ta ) ) )
2		ax-frege8 38103	. 2 |- ( ( ( ( ps -> ch ) /\ ( th -> ta ) ) -> (if- ( ph , ps , th ) -> if- ( ph , ch , ta ) ) ) -> (if- ( ph , ps , th ) -> ( ( ( ps -> ch ) /\ ( th -> ta ) ) -> if- ( ph , ch , ta ) ) ) )
3	1, 2	ax-mp 5	1 |- (if- ( ph , ps , th ) -> ( ( ( ps -> ch ) /\ ( th -> ta ) ) -> 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-frege8 38103  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:  frege63a  38175  frege64a  38176