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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 3776 | . 2 ⊢ 𝐵 ⊆ (𝐵 ∪ 𝐶) | |
2 | bnj931.1 | . 2 ⊢ 𝐴 = (𝐵 ∪ 𝐶) | |
3 | 1, 2 | sseqtr4i 3638 | 1 ⊢ 𝐵 ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 ∪ cun 3572 ⊆ wss 3574 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-in 3581 df-ss 3588 |
This theorem is referenced by: bnj945 30844 bnj545 30965 bnj548 30967 bnj570 30975 bnj929 31006 bnj1136 31065 bnj1408 31104 bnj1442 31117 |
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