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Axiom ax-frege52c 36555
Description: One side of dfsbcq 3257. Part of Axiom 52 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.)
Assertion
Ref Expression
ax-frege52c  |-  ( A  =  B  ->  ( [. A  /  x ]. ph  ->  [. B  /  x ]. ph ) )

Detailed syntax breakdown of Axiom ax-frege52c
StepHypRef Expression
1 cA . . 3  class  A
2 cB . . 3  class  B
31, 2wceq 1452 . 2  wff  A  =  B
4 wph . . . 4  wff  ph
5 vx . . . 4  setvar  x
64, 5, 1wsbc 3255 . . 3  wff  [. A  /  x ]. ph
74, 5, 2wsbc 3255 . . 3  wff  [. B  /  x ]. ph
86, 7wi 4 . 2  wff  ( [. A  /  x ]. ph  ->  [. B  /  x ]. ph )
93, 8wi 4 1  wff  ( A  =  B  ->  ( [. A  /  x ]. ph  ->  [. B  /  x ]. ph ) )
Colors of variables: wff setvar class
This axiom is referenced by:  frege52b  36556  frege53c  36581  frege57c  36587
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