![]() |
Mathbox for Richard Penner |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > rp-abid | Structured version Visualization version GIF version |
Description: Two ways to express a class. (Contributed by RP, 13-Feb-2025.) |
Ref | Expression |
---|---|
rp-abid | ⊢ 𝐴 = {𝑥 ∣ ∃𝑎 ∈ 𝐴 𝑥 = 𝑎} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clel5 3664 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ ∃𝑎 ∈ 𝐴 𝑥 = 𝑎) | |
2 | 1 | eqabi 2874 | 1 ⊢ 𝐴 = {𝑥 ∣ ∃𝑎 ∈ 𝐴 𝑥 = 𝑎} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1536 {cab 2711 ∃wrex 3067 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1539 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-rex 3068 |
This theorem is referenced by: oaun2 43370 oaun3 43371 |
Copyright terms: Public domain | W3C validator |