Theorem dffunsALTV 39417

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 39415	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 39414	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 38903	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

Syntax hints:   = wceq 1570   ∈ wcel 2143  {crab 3416   ≀ ccoss 38832   Rels crels 38834   CnvRefRels ccnvrefrels 38840   Funss cfunss 38863   FunsALTV cfunsALTV 38864

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3417  df-v 3457  df-in 3912  df-funss 39414  df-funsALTV 39415

This theorem is referenced by:  dffunsALTV2  39418  dffunsALTV3  39419  dffunsALTV4  39420  elfunsALTV  39426