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 cosselrels 
 |-  ( f e. Rels -> ,~ f e. Rels )
3 2 biantrud 
 |-  ( f e. Rels -> ( ,~ f C_ _I <-> ( ,~ f C_ _I /\ ,~ f e. Rels ) ) )
4 cosselcnvrefrels2 
 |-  ( ,~ f e. CnvRefRels <-> ( ,~ f C_ _I /\ ,~ f e. Rels ) )
5 3 4 syl6rbbr 
 |-  ( f e. Rels -> ( ,~ f e. CnvRefRels <-> ,~ f C_ _I ) )
6 1 5 rabimbieq 
 |-  FunsALTV = { f e. Rels | ,~ f C_ _I }