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 | abeq2i 2945 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ 𝜑) |
3 | 2 | biimpi 217 | 1 ⊢ (𝑥 ∈ 𝐴 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1528 ∈ wcel 2105 {cab 2796 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-12 2167 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-tru 1531 df-ex 1772 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 |
This theorem is referenced by: bnj1517 32021 bnj66 32031 bnj900 32100 bnj1296 32190 bnj1371 32198 bnj1374 32200 bnj1398 32203 bnj1450 32219 bnj1497 32229 bnj1498 32230 bnj1514 32232 bnj1501 32236 |
Copyright terms: Public domain | W3C validator |