Theorem dffunsALTV 38665

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 38663	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 38662	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38234	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1537   ∈ wcel 2106  {crab 3433   ≀ ccoss 38162   Rels crels 38164   CnvRefRels ccnvrefrels 38170   Funss cfunss 38191   FunsALTV cfunsALTV 38192

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-in 3970  df-funss 38662  df-funsALTV 38663

This theorem is referenced by:  dffunsALTV2  38666  dffunsALTV3  38667  dffunsALTV4  38668  elfunsALTV  38674