Metamath Proof Explorer


Theorem dffunsALTV2

Description: Alternate definition of the class of functions. (Contributed by Peter Mazsa, 30-Aug-2021)

Ref Expression
Assertion dffunsALTV2
|- FunsALTV = { f e. Rels | ,~ f C_ _I }

Proof

Step Hyp Ref Expression
1 dffunsALTV
 |-  FunsALTV = { f e. Rels | ,~ f e. CnvRefRels }
2 cosselcnvrefrels2
 |-  ( ,~ f e. CnvRefRels <-> ( ,~ f C_ _I /\ ,~ f e. Rels ) )
3 cosselrels
 |-  ( f e. Rels -> ,~ f e. Rels )
4 3 biantrud
 |-  ( f e. Rels -> ( ,~ f C_ _I <-> ( ,~ f C_ _I /\ ,~ f e. Rels ) ) )
5 2 4 bitr4id
 |-  ( f e. Rels -> ( ,~ f e. CnvRefRels <-> ,~ f C_ _I ) )
6 1 5 rabimbieq
 |-  FunsALTV = { f e. Rels | ,~ f C_ _I }