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Theorem dffunsALTV 37195
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
StepHypRef Expression
1 df-funsALTV 37193 . 2 FunsALTV = ( Funss ∩ Rels )
2 df-funss 37192 . 2 Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
31, 2abeqin 36762 1 FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  wcel 2107  {crab 3406  ccoss 36684   Rels crels 36686   CnvRefRels ccnvrefrels 36692   Funss cfunss 36713   FunsALTV cfunsALTV 36714
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3407  df-v 3449  df-in 3921  df-funss 37192  df-funsALTV 37193
This theorem is referenced by:  dffunsALTV2  37196  dffunsALTV3  37197  dffunsALTV4  37198  elfunsALTV  37204
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