Metamath Proof Explorer


Theorem abid2f

Description: A simplification of class abstraction. Theorem 5.2 of Quine p. 35. (Contributed by NM, 5-Sep-2011) (Revised by Mario Carneiro, 7-Oct-2016) (Proof shortened by Wolf Lammen, 26-Feb-2025)

Ref Expression
Hypothesis abid2f.1 _xA
Assertion abid2f x|xA=A

Proof

Step Hyp Ref Expression
1 abid2f.1 _xA
2 1 eqabf A=x|xAxxAxA
3 biid xAxA
4 2 3 mpgbir A=x|xA
5 4 eqcomi x|xA=A