Metamath Proof Explorer


Theorem abid2fOLD

Description: Obsolete version of abid2f as of 26-Feb-2025. (Contributed by NM, 5-Sep-2011) (Revised by Mario Carneiro, 7-Oct-2016) (Proof shortened by Wolf Lammen, 17-Nov-2019) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis abid2f.1 _ x A
Assertion abid2fOLD x | x A = A

Proof

Step Hyp Ref Expression
1 abid2f.1 _ x A
2 nfab1 _ x x | x A
3 2 1 cleqf x | x A = A x x x | x A x A
4 abid x x | x A x A
5 3 4 mpgbir x | x A = A