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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj931 | 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 |
|---|---|
| bnj931.1 | ⊢ 𝐴 = (𝐵 ∪ 𝐶) |
| Ref | Expression |
|---|---|
| bnj931 | ⊢ 𝐵 ⊆ 𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ssun1 4178 | . 2 ⊢ 𝐵 ⊆ (𝐵 ∪ 𝐶) | |
| 2 | bnj931.1 | . 2 ⊢ 𝐴 = (𝐵 ∪ 𝐶) | |
| 3 | 1, 2 | sseqtrri 4033 | 1 ⊢ 𝐵 ⊆ 𝐴 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ∪ cun 3949 ⊆ wss 3951 |
| 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-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-un 3956 df-ss 3968 |
| This theorem is referenced by: bnj945 34787 bnj545 34909 bnj548 34911 bnj570 34919 bnj929 34950 bnj1136 35011 bnj1408 35050 bnj1442 35063 |
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