Theorem dffunsALTV 39966

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 39964	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 39963	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 39452	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

This proof depends on syntax axioms:   = wceq 1570   ∈ wcel 2147  {crab 3416   ≀ ccoss 39381   Rels crels 39383   CnvRefRels ccnvrefrels 39389   Funss cfunss 39412   FunsALTV cfunsALTV 39413

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-in 4094  df-funss 39963  df-funsALTV 39964

This theorem is used by:  dffunsALTV2  39967  dffunsALTV3  39968  dffunsALTV4  39969  elfunsALTV  39975