Theorem dffunsALTV 39267

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 39265	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 39264	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38753	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1560   ∈ wcel 2142  {crab 3414   ≀ ccoss 38682   Rels crels 38684   CnvRefRels ccnvrefrels 38690   Funss cfunss 38713   FunsALTV cfunsALTV 38714

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1563  df-ex 1800  df-sb 2091  df-clab 2741  df-cleq 2754  df-clel 2837  df-rab 3415  df-v 3456  df-in 3911  df-funss 39264  df-funsALTV 39265

This theorem is referenced by:  dffunsALTV2  39268  dffunsALTV3  39269  dffunsALTV4  39270  elfunsALTV  39276