Theorem frege3 38089

Description: Add antecedent to ax-frege2 38085. Special case of rp-frege3g 38088. Proposition 3 of [Frege1879] p. 29. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege3	|- ( ( ph -> ps ) -> ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) )

Proof of Theorem frege3

Step	Hyp	Ref	Expression
1		ax-frege2 38085	. 2 |- ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) )
2		ax-frege1 38084	. 2 |- ( ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) -> ( ( ph -> ps ) -> ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ps ) -> ( ( ch -> ( 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:  frege4  38093