Theorem dffunsALTV 38684

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 38682	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 38681	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38253	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1540   ∈ wcel 2108  {crab 3436   ≀ ccoss 38182   Rels crels 38184   CnvRefRels ccnvrefrels 38190   Funss cfunss 38211   FunsALTV cfunsALTV 38212

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-in 3958  df-funss 38681  df-funsALTV 38682

This theorem is referenced by:  dffunsALTV2  38685  dffunsALTV3  38686  dffunsALTV4  38687  elfunsALTV  38693