Theorem dffunsALTV 38881

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 38879	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 38878	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38389	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1541   ∈ wcel 2113  {crab 3397   ≀ ccoss 38322   Rels crels 38324   CnvRefRels ccnvrefrels 38330   Funss cfunss 38351   FunsALTV cfunsALTV 38352

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-rab 3398  df-v 3440  df-in 3906  df-funss 38878  df-funsALTV 38879

This theorem is referenced by:  dffunsALTV2  38882  dffunsALTV3  38883  dffunsALTV4  38884  elfunsALTV  38890