Theorem dffunsALTV 38682

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 38680	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 38679	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38248	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1540   ∈ wcel 2109  {crab 3408   ≀ ccoss 38176   Rels crels 38178   CnvRefRels ccnvrefrels 38184   Funss cfunss 38205   FunsALTV cfunsALTV 38206

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 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3409  df-v 3452  df-in 3924  df-funss 38679  df-funsALTV 38680

This theorem is referenced by:  dffunsALTV2  38683  dffunsALTV3  38684  dffunsALTV4  38685  elfunsALTV  38691