Metamath Proof Explorer

Theorem funopabeq

Description: A class of ordered pairs of values is a function. (Contributed by NM, 14-Nov-1995)

Ref Expression
Assertion funopabeq 
|- Fun { <. x , y >. | y = A }

Proof

Step Hyp Ref Expression
1 funopab 
 |-  ( Fun { <. x , y >. | y = A } <-> A. x E* y y = A )
2 moeq 
 |-  E* y y = A
3 1 2 mpgbir 
 |-  Fun { <. x , y >. | y = A }