Theorem frege4 38093

Description: Special case of closed form of a2d 29. Special case of rp-frege4g 38092. Proposition 4 of [Frege1879] p. 31. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege4	|- ( ( ( ph -> ps ) -> ( ch -> ( ph -> ps ) ) ) -> ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) )

Proof of Theorem frege4

Step	Hyp	Ref	Expression
1		frege3 38089	. 2 |- ( ( ph -> ps ) -> ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) )
2		ax-frege2 38085	. 2 |- ( ( ( ph -> ps ) -> ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) ) -> ( ( ( ph -> ps ) -> ( ch -> ( ph -> ps ) ) ) -> ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ( ph -> ps ) -> ( ch -> ( ph -> ps ) ) ) -> ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085

This theorem is referenced by:  frege5  38094