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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1517 | 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 |
---|---|
bnj1517.1 | ⊢ 𝐴 = {𝑥 ∣ (𝜑 ∧ 𝜓)} |
Ref | Expression |
---|---|
bnj1517 | ⊢ (𝑥 ∈ 𝐴 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1517.1 | . . 3 ⊢ 𝐴 = {𝑥 ∣ (𝜑 ∧ 𝜓)} | |
2 | 1 | bnj1436 30910 | . 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 ∧ 𝜓)) |
3 | 2 | simprd 479 | 1 ⊢ (𝑥 ∈ 𝐴 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 = wceq 1483 ∈ wcel 1990 {cab 2608 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-12 2047 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-tru 1486 df-ex 1705 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 |
This theorem is referenced by: bnj1286 31087 bnj1450 31118 bnj1501 31135 |
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