Theorem dffunsALTV 36721

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 36719	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 36718	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 36319	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1539   ∈ wcel 2108  {crab 3067   ≀ ccoss 36260   Rels crels 36262   CnvRefRels ccnvrefrels 36268   Funss cfunss 36289   FunsALTV cfunsALTV 36290

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3072  df-v 3424  df-in 3890  df-funss 36718  df-funsALTV 36719

This theorem is referenced by:  dffunsALTV2  36722  dffunsALTV3  36723  dffunsALTV4  36724  elfunsALTV  36730