Theorem dffunsALTV 37645

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 37643	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 37642	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 37212	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1541   ∈ wcel 2106  {crab 3432   ≀ ccoss 37135   Rels crels 37137   CnvRefRels ccnvrefrels 37143   Funss cfunss 37164   FunsALTV cfunsALTV 37165

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rab 3433  df-v 3476  df-in 3955  df-funss 37642  df-funsALTV 37643

This theorem is referenced by:  dffunsALTV2  37646  dffunsALTV3  37647  dffunsALTV4  37648  elfunsALTV  37654