Metamath Proof Explorer


Theorem clelsb1fw

Description: Substitution for the first argument of the membership predicate in an atomic formula (class version of elsb1 ). Version of clelsb1f with a disjoint variable condition, which does not require ax-13 . (Contributed by Rodolfo Medina, 28-Apr-2010) Avoid ax-13 . (Revised by Gino Giotto, 10-Jan-2024)

Ref Expression
Hypothesis clelsb1fw.1 _xA
Assertion clelsb1fw yxxAyA

Proof

Step Hyp Ref Expression
1 clelsb1fw.1 _xA
2 1 nfcri xwA
3 2 sbco2v yxxwwAywwA
4 clelsb1 xwwAxA
5 4 sbbii yxxwwAyxxA
6 clelsb1 ywwAyA
7 3 5 6 3bitr3i yxxAyA