Metamath Proof Explorer

Theorem frege61b

Description: Lemma for frege65b . Proposition 61 of Frege1879 p. 52. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege61b 
|- ( ( [ x / y ] ph -> ps ) -> ( A. y ph -> ps ) )

Proof

Step Hyp Ref Expression
1 ax-frege58b 
 |-  ( A. y ph -> [ x / y ] ph )
2 frege9 
 |-  ( ( A. y ph -> [ x / y ] ph ) -> ( ( [ x / y ] ph -> ps ) -> ( A. y ph -> ps ) ) )
3 1 2 ax-mp 
 |-  ( ( [ x / y ] ph -> ps ) -> ( A. y ph -> ps ) )