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Mathbox for Jonathan Ben-Naim |
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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 3738 | . 2 ⊢ 𝐵 ⊆ (𝐵 ∪ 𝐶) | |
2 | bnj931.1 | . 2 ⊢ 𝐴 = (𝐵 ∪ 𝐶) | |
3 | 1, 2 | sseqtr4i 3601 | 1 ⊢ 𝐵 ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∪ cun 3538 ⊆ wss 3540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-un 3545 df-in 3547 df-ss 3554 |
This theorem is referenced by: bnj945 30098 bnj545 30219 bnj548 30221 bnj570 30229 bnj929 30260 bnj1136 30319 bnj1408 30358 bnj1442 30371 |
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