Theorem dffunsALTV 38942

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 38940	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 38939	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38450	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1541   ∈ wcel 2113  {crab 3399   ≀ ccoss 38383   Rels crels 38385   CnvRefRels ccnvrefrels 38391   Funss cfunss 38412   FunsALTV cfunsALTV 38413

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 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3400  df-v 3442  df-in 3908  df-funss 38939  df-funsALTV 38940

This theorem is referenced by:  dffunsALTV2  38943  dffunsALTV3  38944  dffunsALTV4  38945  elfunsALTV  38951