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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj918 | 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 |
---|---|
bnj918.1 | ⊢ 𝐺 = (𝑓 ∪ {〈𝑛, 𝐶〉}) |
Ref | Expression |
---|---|
bnj918 | ⊢ 𝐺 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj918.1 | . 2 ⊢ 𝐺 = (𝑓 ∪ {〈𝑛, 𝐶〉}) | |
2 | vex 3176 | . . 3 ⊢ 𝑓 ∈ V | |
3 | snex 4835 | . . 3 ⊢ {〈𝑛, 𝐶〉} ∈ V | |
4 | 2, 3 | unex 6854 | . 2 ⊢ (𝑓 ∪ {〈𝑛, 𝐶〉}) ∈ V |
5 | 1, 4 | eqeltri 2684 | 1 ⊢ 𝐺 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∈ wcel 1977 Vcvv 3173 ∪ cun 3538 {csn 4125 〈cop 4131 |
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-8 1979 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pr 4833 ax-un 6847 |
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-rex 2902 df-v 3175 df-dif 3543 df-un 3545 df-nul 3875 df-sn 4126 df-pr 4128 df-uni 4373 |
This theorem is referenced by: bnj528 30213 bnj929 30260 bnj965 30266 bnj910 30272 bnj985 30277 bnj999 30281 bnj1018 30286 bnj907 30289 |
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