Theorem dffunsALTV 38159

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 38157	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 38156	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 37728	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1533   ∈ wcel 2098  {crab 3428   ≀ ccoss 37653   Rels crels 37655   CnvRefRels ccnvrefrels 37661   Funss cfunss 37682   FunsALTV cfunsALTV 37683

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-rab 3429  df-v 3473  df-in 3954  df-funss 38156  df-funsALTV 38157

This theorem is referenced by:  dffunsALTV2  38160  dffunsALTV3  38161  dffunsALTV4  38162  elfunsALTV  38168