![]() |
Mathbox for Peter Mazsa |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > dffunsALTV | Structured version Visualization version GIF version |
Description: Alternate definition of the class of functions. (Contributed by Peter Mazsa, 18-Jul-2021.) |
Ref | Expression |
---|---|
dffunsALTV | ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-funsALTV 38157 | . 2 ⊢ FunsALTV = ( Funss ∩ Rels ) | |
2 | df-funss 38156 | . 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels } | |
3 | 1, 2 | abeqin 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 |