Theorem dffunsALTV 37553

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 37551	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 37550	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 37120	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1542   ∈ wcel 2107  {crab 3433   ≀ ccoss 37043   Rels crels 37045   CnvRefRels ccnvrefrels 37051   Funss cfunss 37072   FunsALTV cfunsALTV 37073

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-in 3956  df-funss 37550  df-funsALTV 37551

This theorem is referenced by:  dffunsALTV2  37554  dffunsALTV3  37555  dffunsALTV4  37556  elfunsALTV  37562