Metamath Proof Explorer


Theorem bj-ssbid2ALT

Description: Alternate proof of bj-ssbid2 , not using sbequ2 . (Contributed by BJ, 22-Dec-2020) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion bj-ssbid2ALT xxφφ

Proof

Step Hyp Ref Expression
1 df-sb xxφyy=xxx=yφ
2 sp xx=yφx=yφ
3 2 imim2i y=xxx=yφy=xx=yφ
4 3 alimi yy=xxx=yφyy=xx=yφ
5 pm2.21 ¬y=xy=xφ
6 equcomi y=xx=y
7 6 imim1i x=yφy=xφ
8 5 7 ja y=xx=yφy=xφ
9 8 alimi yy=xx=yφyy=xφ
10 ax6ev yy=x
11 19.23v yy=xφyy=xφ
12 11 biimpi yy=xφyy=xφ
13 9 10 12 mpisyl yy=xx=yφφ
14 4 13 syl yy=xxx=yφφ
15 1 14 sylbi xxφφ