Theorem dffunsALTV 39306

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 39304	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 39303	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38792	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1567   ∈ wcel 2149  {crab 3423   ≀ ccoss 38721   Rels crels 38723   CnvRefRels ccnvrefrels 38729   Funss cfunss 38752   FunsALTV cfunsALTV 38753

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-rab 3424  df-v 3465  df-in 3920  df-funss 39303  df-funsALTV 39304

This theorem is referenced by:  dffunsALTV2  39307  dffunsALTV3  39308  dffunsALTV4  39309  elfunsALTV  39315