Metamath Proof Explorer


Theorem dffunsALTV4

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 E* y1 x1 f y1 } . (Contributed by Peter Mazsa, 31-Aug-2021)

Ref Expression
Assertion dffunsALTV4 FunsALTV = f Rels | u * x u f x

Proof

Step Hyp Ref Expression
1 dffunsALTV FunsALTV = f Rels | f CnvRefRels
2 cosselcnvrefrels4 f CnvRefRels u * x u f x f Rels
3 cosselrels f Rels f Rels
4 3 biantrud f Rels u * x u f x u * x u f x f Rels
5 2 4 bitr4id f Rels f CnvRefRels u * x u f x
6 1 5 rabimbieq FunsALTV = f Rels | u * x u f x