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Mathbox for Jonathan Ben-Naim |
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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 3492 | . . 3 ⊢ 𝑓 ∈ V | |
3 | snex 5451 | . . 3 ⊢ {〈𝑛, 𝐶〉} ∈ V | |
4 | 2, 3 | unex 7781 | . 2 ⊢ (𝑓 ∪ {〈𝑛, 𝐶〉}) ∈ V |
5 | 1, 4 | eqeltri 2840 | 1 ⊢ 𝐺 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ∈ wcel 2108 Vcvv 3488 ∪ cun 3974 {csn 4648 〈cop 4654 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2711 ax-sep 5317 ax-nul 5324 ax-pr 5447 ax-un 7772 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-tru 1540 df-fal 1550 df-ex 1778 df-sb 2065 df-clab 2718 df-cleq 2732 df-clel 2819 df-v 3490 df-dif 3979 df-un 3981 df-ss 3993 df-nul 4353 df-sn 4649 df-pr 4651 df-uni 4932 |
This theorem is referenced by: bnj528 34867 bnj929 34914 bnj965 34920 bnj910 34926 bnj985v 34931 bnj985 34932 bnj999 34936 bnj1018g 34941 bnj1018 34942 bnj907 34945 |
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