Theorem frege27 38105

Description: We cannot (at the same time) affirm ph and deny ph. Identical to id 22. Proposition 27 of [Frege1879] p. 43. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege27	|- ( ph -> ph )

Proof of Theorem frege27

Step	Hyp	Ref	Expression
1		ax-frege1 38084	. 2 |- ( ph -> ( ps -> ph ) )
2		frege26 38104	. 2 |- ( ( ph -> ( ps -> ph ) ) -> ( ph -> ph ) )
3	1, 2	ax-mp 5	1 |- ( ph -> ph )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege8 38103

This theorem is referenced by:  frege42  38140