![]() |
Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
|
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 4188 | . 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 1537 ∪ cun 3961 ⊆ wss 3963 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-v 3480 df-un 3968 df-ss 3980 |
This theorem is referenced by: bnj945 34766 bnj545 34888 bnj548 34890 bnj570 34898 bnj929 34929 bnj1136 34990 bnj1408 35029 bnj1442 35042 |
Copyright terms: Public domain | W3C validator |