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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 4159 | . 2 ⊢ 𝐵 ⊆ (𝐵 ∪ 𝐶) | |
2 | bnj931.1 | . 2 ⊢ 𝐴 = (𝐵 ∪ 𝐶) | |
3 | 1, 2 | sseqtrri 4006 | 1 ⊢ 𝐵 ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 ∪ cun 3933 ⊆ wss 3935 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2709 df-cleq 2723 df-clel 2809 df-v 3468 df-un 3940 df-in 3942 df-ss 3952 |
This theorem is referenced by: bnj945 33515 bnj545 33637 bnj548 33639 bnj570 33647 bnj929 33678 bnj1136 33739 bnj1408 33778 bnj1442 33791 |
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