Theorem dffunsALTV 39700

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 39698	. 2 ⊢ FunsALTV = ( Funss ∩ Rels )
2		df-funss 39697	. 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
3	1, 2	abeqin 39186	1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }

This proof depends on syntax axioms:   = wceq 1570   ∈ wcel 2145  {crab 3413   ≀ ccoss 39115   Rels crels 39117   CnvRefRels ccnvrefrels 39123   Funss cfunss 39146   FunsALTV cfunsALTV 39147

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2733

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3414  df-v 3453  df-in 3906  df-funss 39697  df-funsALTV 39698

This theorem is used by:  dffunsALTV2  39701  dffunsALTV3  39702  dffunsALTV4  39703  elfunsALTV  39709