Metamath Proof Explorer

Theorem frege57b

Description: Analogue of frege57aid . Proposition 57 of Frege1879 p. 51. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege57b 
|- ( x = y -> ( [ y / z ] ph -> [ x / z ] ph ) )

Proof

Step Hyp Ref Expression
1 frege52b 
 |-  ( y = x -> ( [ y / z ] ph -> [ x / z ] ph ) )
2 frege56b 
 |-  ( ( y = x -> ( [ y / z ] ph -> [ x / z ] ph ) ) -> ( x = y -> ( [ y / z ] ph -> [ x / z ] ph ) ) )
3 1 2 ax-mp 
 |-  ( x = y -> ( [ y / z ] ph -> [ x / z ] ph ) )