Theorem dffunsALTV 39135

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 39133	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 39132	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38621	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1547   ∈ wcel 2119  {crab 3391   ≀ ccoss 38550   Rels crels 38552   CnvRefRels ccnvrefrels 38558   Funss cfunss 38581   FunsALTV cfunsALTV 38582

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-rab 3392  df-v 3433  df-in 3890  df-funss 39132  df-funsALTV 39133

This theorem is referenced by:  dffunsALTV2  39136  dffunsALTV3  39137  dffunsALTV4  39138  elfunsALTV  39144