|   | 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 38682 | . 2 ⊢ FunsALTV = ( Funss ∩ Rels ) | |
| 2 | df-funss 38681 | . 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels } | |
| 3 | 1, 2 | abeqin 38253 | 1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels } | 
| Colors of variables: wff setvar class | 
| Syntax hints: = wceq 1540 ∈ wcel 2108 {crab 3436 ≀ ccoss 38182 Rels crels 38184 CnvRefRels ccnvrefrels 38190 Funss cfunss 38211 FunsALTV cfunsALTV 38212 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-v 3482 df-in 3958 df-funss 38681 df-funsALTV 38682 | 
| This theorem is referenced by: dffunsALTV2 38685 dffunsALTV3 38686 dffunsALTV4 38687 elfunsALTV 38693 | 
| Copyright terms: Public domain | W3C validator |