Theorem dffunsALTV 37857

Description: Alternate definition of the class of functions. (Contributed by Peter Mazsa, 18-Jul-2021.)

Assertion

Ref	Expression
dffunsALTV	⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Proof of Theorem dffunsALTV

Step	Hyp	Ref	Expression
1		df-funsALTV 37855	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 37854	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 37424	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1540   ∈ wcel 2105  {crab 3431   ≀ ccoss 37347   Rels crels 37349   CnvRefRels ccnvrefrels 37355   Funss cfunss 37376   FunsALTV cfunsALTV 37377

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3432  df-v 3475  df-in 3955  df-funss 37854  df-funsALTV 37855

This theorem is referenced by:  dffunsALTV2  37858  dffunsALTV3  37859  dffunsALTV4  37860  elfunsALTV  37866