Theorem frege66b 38205

Description: Swap antecedents of frege65b 38204. Proposition 66 of [Frege1879] p. 54. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege66b	|- ( A. x ( ph -> ps ) -> ( A. x ( ch -> ph ) -> ( [ y / x ] ch -> [ y / x ] ps ) ) )

Proof of Theorem frege66b

Step	Hyp	Ref	Expression
1		frege65b 38204	. 2 |- ( A. x ( ch -> ph ) -> ( A. x ( ph -> ps ) -> ( [ y / x ] ch -> [ y / x ] ps ) ) )
2		ax-frege8 38103	. 2 |- ( ( A. x ( ch -> ph ) -> ( A. x ( ph -> ps ) -> ( [ y / x ] ch -> [ y / x ] ps ) ) ) -> ( A. x ( ph -> ps ) -> ( A. x ( ch -> ph ) -> ( [ y / x ] ch -> [ y / x ] ps ) ) ) )
3	1, 2	ax-mp 5	1 |- ( A. x ( ph -> ps ) -> ( A. x ( ch -> ph ) -> ( [ y / x ] ch -> [ y / x ] ps ) ) )

Syntax hints:   -> wi 4   A.wal 1481   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246  ax-frege1 38084  ax-frege2 38085  ax-frege8 38103  ax-frege58b 38195

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by: (None)