Theorem frege68a 38180

Description: Combination of applying a definition and applying it to a specific instance. Proposition 68 of [Frege1879] p. 54. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege68a	|- ( ( ( ps /\ ch ) <-> th ) -> ( th -> if- ( ph , ps , ch ) ) )

Proof of Theorem frege68a

Step	Hyp	Ref	Expression
1		frege57aid 38166	. 2 |- ( ( ( ps /\ ch ) <-> th ) -> ( th -> ( ps /\ ch ) ) )
2		frege67a 38179	. 2 |- ( ( ( ( ps /\ ch ) <-> th ) -> ( th -> ( ps /\ ch ) ) ) -> ( ( ( ps /\ ch ) <-> th ) -> ( th -> if- ( ph , ps , ch ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ( ps /\ ch ) <-> th ) -> ( th -> if- ( ph , ps , ch ) ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384  if-wif 1012

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 38084  ax-frege2 38085  ax-frege8 38103  ax-frege52a 38151  ax-frege58a 38169

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ifp 1013  df-tru 1486  df-fal 1489

This theorem is referenced by: (None)