Metamath Proof Explorer

Theorem dfiin2

Description: Alternate definition of indexed intersection when B is a set. Definition 15(b) of Suppes p. 44. (Contributed by NM, 28-Jun-1998) (Proof shortened by Andrew Salmon, 25-Jul-2011)

Ref Expression
Hypothesis dfiun2.1 B V
Assertion dfiin2 x A B = y | x A y = B


Step Hyp Ref Expression
1 dfiun2.1 B V
2 dfiin2g x A B V x A B = y | x A y = B
3 1 a1i x A B V
4 2 3 mprg x A B = y | x A y = B