Theorem dffunsALTV 39089

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 39087	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 39086	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38575	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1542   ∈ wcel 2114  {crab 3389   ≀ ccoss 38504   Rels crels 38506   CnvRefRels ccnvrefrels 38512   Funss cfunss 38535   FunsALTV cfunsALTV 38536

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3390  df-v 3431  df-in 3896  df-funss 39086  df-funsALTV 39087

This theorem is referenced by:  dffunsALTV2  39090  dffunsALTV3  39091  dffunsALTV4  39092  elfunsALTV  39098