Metamath Proof Explorer

Theorem frege55lem1a

Description: Necessary deduction regarding substitution of value in equality. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege55lem1a 
|- ( ( ta -> if- ( ps , ph , -. ph ) ) -> ( ta -> ( ps <-> ph ) ) )

Proof

Step Hyp Ref Expression
1 frege54cor0a 
 |-  ( ( ps <-> ph ) <-> if- ( ps , ph , -. ph ) )
2 1 biimpri 
 |-  ( if- ( ps , ph , -. ph ) -> ( ps <-> ph ) )
3 2 imim2i 
 |-  ( ( ta -> if- ( ps , ph , -. ph ) ) -> ( ta -> ( ps <-> ph ) ) )