Theorem dffunsALTV 38729

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 38727	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 38726	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38295	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1541   ∈ wcel 2111  {crab 3395   ≀ ccoss 38223   Rels crels 38225   CnvRefRels ccnvrefrels 38231   Funss cfunss 38252   FunsALTV cfunsALTV 38253

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 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-rab 3396  df-v 3438  df-in 3904  df-funss 38726  df-funsALTV 38727

This theorem is referenced by:  dffunsALTV2  38730  dffunsALTV3  38731  dffunsALTV4  38732  elfunsALTV  38738