![]() |
Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1292 | 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 |
---|---|
bnj1292.1 | ⊢ 𝐴 = (𝐵 ∩ 𝐶) |
Ref | Expression |
---|---|
bnj1292 | ⊢ 𝐴 ⊆ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1292.1 | . 2 ⊢ 𝐴 = (𝐵 ∩ 𝐶) | |
2 | inss1 4224 | . 2 ⊢ (𝐵 ∩ 𝐶) ⊆ 𝐵 | |
3 | 1, 2 | eqsstri 4012 | 1 ⊢ 𝐴 ⊆ 𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1534 ∩ cin 3943 ⊆ wss 3944 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2698 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1537 df-ex 1775 df-sb 2061 df-clab 2705 df-cleq 2719 df-clel 2805 df-v 3471 df-in 3951 df-ss 3961 |
This theorem is referenced by: bnj1253 34584 bnj1286 34586 bnj1280 34587 bnj1296 34588 |
Copyright terms: Public domain | W3C validator |