Theorem dffunsALTV 38639

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 38637	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 38636	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38208	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1537   ∈ wcel 2108  {crab 3443   ≀ ccoss 38135   Rels crels 38137   CnvRefRels ccnvrefrels 38143   Funss cfunss 38164   FunsALTV cfunsALTV 38165

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-v 3490  df-in 3983  df-funss 38636  df-funsALTV 38637

This theorem is referenced by:  dffunsALTV2  38640  dffunsALTV3  38641  dffunsALTV4  38642  elfunsALTV  38648