Users' Mathboxes Mathbox for Peter Mazsa < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dffunsALTV Structured version   Visualization version   GIF version

Theorem dffunsALTV 38159
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 38157 . 2 FunsALTV = ( Funss ∩ Rels )
2 df-funss 38156 . 2 Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels }
31, 2abeqin 37728 1 FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels }
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wcel 2098  {crab 3428  ccoss 37653   Rels crels 37655   CnvRefRels ccnvrefrels 37661   Funss cfunss 37682   FunsALTV cfunsALTV 37683
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-rab 3429  df-v 3473  df-in 3954  df-funss 38156  df-funsALTV 38157
This theorem is referenced by:  dffunsALTV2  38160  dffunsALTV3  38161  dffunsALTV4  38162  elfunsALTV  38168
  Copyright terms: Public domain W3C validator