Theorem frege53aid 38153

Description: Specialization of frege53a 38154. Proposition 53 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege53aid	|- ( ph -> ( ( ph <-> ps ) -> ps ) )

Proof of Theorem frege53aid

Step	Hyp	Ref	Expression
1		frege52aid 38152	. 2 |- ( ( ph <-> ps ) -> ( ph -> ps ) )
2		ax-frege8 38103	. 2 |- ( ( ( ph <-> ps ) -> ( ph -> ps ) ) -> ( ph -> ( ( ph <-> ps ) -> ps ) ) )
3	1, 2	ax-mp 5	1 |- ( ph -> ( ( ph <-> ps ) -> ps ) )

Syntax hints:   -> wi 4   <-> wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege8 38103  ax-frege52a 38151

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)