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Mathbox for Jonathan Ben-Naim |
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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 2869 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ 𝜑) |
3 | 2 | biimpi 215 | 1 ⊢ (𝑥 ∈ 𝐴 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1533 ∈ wcel 2098 {cab 2702 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-12 2166 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 |
This theorem is referenced by: bnj1517 34612 bnj66 34622 bnj900 34691 bnj1296 34783 bnj1371 34791 bnj1374 34793 bnj1398 34796 bnj1450 34812 bnj1497 34822 bnj1498 34823 bnj1514 34825 bnj1501 34829 |
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