Metamath Proof Explorer


Theorem sbco

Description: A composition law for substitution. Usage of this theorem is discouraged because it depends on ax-13 . See sbcov for a version with a disjoint variable condition requiring fewer axioms. (Contributed by NM, 14-May-1993) (Proof shortened by Wolf Lammen, 21-Sep-2018) (New usage is discouraged.)

Ref Expression
Assertion sbco yxxyφyxφ

Proof

Step Hyp Ref Expression
1 sbcom3 yxxyφyxyyφ
2 sbid yyφφ
3 2 sbbii yxyyφyxφ
4 1 3 bitri yxxyφyxφ