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 e. Rels | A. u E* x u f x }

Proof

Step	Hyp	Ref	Expression
1		dffunsALTV	|- FunsALTV = { f e. Rels | ,~ f e. CnvRefRels }
2		cosselcnvrefrels4	|- ( ,~ f e. CnvRefRels <-> ( A. u E* x u f x /\ ,~ f e. Rels ) )
3		cosselrels	|- ( f e. Rels -> ,~ f e. Rels )
4	3	biantrud	|- ( f e. Rels -> ( A. u E* x u f x <-> ( A. u E* x u f x /\ ,~ f e. Rels ) ) )
5	2 4	bitr4id	|- ( f e. Rels -> ( ,~ f e. CnvRefRels <-> A. u E* x u f x ) )
6	1 5	rabimbieq	|- FunsALTV = { f e. Rels | A. u E* x u f x }