| Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1436 | Structured version Visualization version GIF version | ||
| Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| bnj1436.1 | ⊢ 𝐴 = {𝑥 ∣ 𝜑} |
| Ref | Expression |
|---|---|
| bnj1436 | ⊢ (𝑥 ∈ 𝐴 → 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bnj1436.1 | . . 3 ⊢ 𝐴 = {𝑥 ∣ 𝜑} | |
| 2 | 1 | eqabri 2885 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ 𝜑) |
| 3 | 2 | biimpi 216 | 1 ⊢ (𝑥 ∈ 𝐴 → 𝜑) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 = wceq 1540 ∈ wcel 2108 {cab 2714 |
| 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-12 2177 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 |
| This theorem is referenced by: bnj1517 34864 bnj66 34874 bnj900 34943 bnj1296 35035 bnj1371 35043 bnj1374 35045 bnj1398 35048 bnj1450 35064 bnj1497 35074 bnj1498 35075 bnj1514 35077 bnj1501 35081 |
| Copyright terms: Public domain | W3C validator |