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Mathbox for Peter Mazsa |
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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 35445 | . 2 ⊢ FunsALTV = ( Funss ∩ Rels ) | |
2 | df-funss 35444 | . 2 ⊢ Funss = {𝑓 ∣ ≀ 𝑓 ∈ CnvRefRels } | |
3 | 1, 2 | abeqin 35046 | 1 ⊢ FunsALTV = {𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels } |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1522 ∈ wcel 2081 {crab 3109 ≀ ccoss 34985 Rels crels 34987 CnvRefRels ccnvrefrels 34993 Funss cfunss 35014 FunsALTV cfunsALTV 35015 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1777 ax-4 1791 ax-5 1888 ax-6 1947 ax-7 1992 ax-8 2083 ax-9 2091 ax-10 2112 ax-11 2126 ax-12 2141 ax-ext 2769 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-tru 1525 df-ex 1762 df-nf 1766 df-sb 2043 df-clab 2776 df-cleq 2788 df-clel 2863 df-nfc 2935 df-rab 3114 df-v 3439 df-in 3866 df-funss 35444 df-funsALTV 35445 |
This theorem is referenced by: dffunsALTV2 35448 dffunsALTV3 35449 dffunsALTV4 35450 elfunsALTV 35456 |
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