Theorem dffunsALTV 39840

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 39838	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 39837	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 39326	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

This proof depends on syntax axioms:   = wceq 1569   ∈ wcel 2146  {crab 3415   ≀ ccoss 39255   Rels crels 39257   CnvRefRels ccnvrefrels 39263   Funss cfunss 39286   FunsALTV cfunsALTV 39287

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3416  df-v 3455  df-in 4093  df-funss 39837  df-funsALTV 39838

This theorem is used by:  dffunsALTV2  39841  dffunsALTV3  39842  dffunsALTV4  39843  elfunsALTV  39849