Metamath Proof Explorer


Theorem dffunsALTV3

Description: Alternate definition of the class of functions. For the X axis and the Y axis you can convert the right side to { f e. Rels | A. x1 A. y1 A. y2 ( ( x1 f y1 /\ x1 f y2 ) -> y1 = y2 ) } . (Contributed by Peter Mazsa, 30-Aug-2021)

Ref Expression
Assertion dffunsALTV3 FunsALTV = f Rels | u x y u f x u f y x = y

Proof

Step Hyp Ref Expression
1 dffunsALTV FunsALTV = f Rels | f CnvRefRels
2 cosselcnvrefrels3 f CnvRefRels u x y u f x u f y x = y f Rels
3 cosselrels f Rels f Rels
4 3 biantrud f Rels u x y u f x u f y x = y u x y u f x u f y x = y f Rels
5 2 4 bitr4id f Rels f CnvRefRels u x y u f x u f y x = y
6 1 5 rabimbieq FunsALTV = f Rels | u x y u f x u f y x = y