Metamath Proof Explorer


Theorem sbcovOLD

Description: Obsolete version of sbcov as of 26-Aug-2025. (Contributed by NM, 14-May-1993) (Revised by GG, 7-Aug-2023) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion sbcovOLD
|- ( [ y / x ] [ x / y ] ph <-> [ y / x ] ph )

Proof

Step Hyp Ref Expression
1 sbcom3vv
 |-  ( [ y / x ] [ x / y ] ph <-> [ y / x ] [ y / y ] ph )
2 sbid
 |-  ( [ y / y ] ph <-> ph )
3 2 sbbii
 |-  ( [ y / x ] [ y / y ] ph <-> [ y / x ] ph )
4 1 3 bitri
 |-  ( [ y / x ] [ x / y ] ph <-> [ y / x ] ph )