Theorem dffunsALTV 36794

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 36792	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 36791	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 36392	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1539   ∈ wcel 2106  {crab 3068   ≀ ccoss 36333   Rels crels 36335   CnvRefRels ccnvrefrels 36341   Funss cfunss 36362   FunsALTV cfunsALTV 36363

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-in 3894  df-funss 36791  df-funsALTV 36792

This theorem is referenced by:  dffunsALTV2  36795  dffunsALTV3  36796  dffunsALTV4  36797  elfunsALTV  36803