Metamath Proof Explorer


Theorem bj-inftyexpiinv

Description: Utility theorem for the inverse of inftyexpi . (Contributed by BJ, 22-Jun-2019) This utility theorem is irrelevant and should generally not be used. (New usage is discouraged.)

Ref Expression
Assertion bj-inftyexpiinv Aππ1stinftyexpiA=A

Proof

Step Hyp Ref Expression
1 opeq1 x=Ax=A
2 df-bj-inftyexpi inftyexpi=xππx
3 opex AV
4 1 2 3 fvmpt AππinftyexpiA=A
5 4 fveq2d Aππ1stinftyexpiA=1stA
6 cnex V
7 op1stg AππV1stA=A
8 6 7 mpan2 Aππ1stA=A
9 5 8 eqtrd Aππ1stinftyexpiA=A