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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj528 | Structured version Visualization version GIF version |
Description: Technical lemma for bnj852 34683. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj528.1 | ⊢ 𝐺 = (𝑓 ∪ {〈𝑚, ∪ 𝑦 ∈ (𝑓‘𝑝) pred(𝑦, 𝐴, 𝑅)〉}) |
Ref | Expression |
---|---|
bnj528 | ⊢ 𝐺 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj528.1 | . 2 ⊢ 𝐺 = (𝑓 ∪ {〈𝑚, ∪ 𝑦 ∈ (𝑓‘𝑝) pred(𝑦, 𝐴, 𝑅)〉}) | |
2 | 1 | bnj918 34528 | 1 ⊢ 𝐺 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∈ wcel 2098 Vcvv 3461 ∪ cun 3942 {csn 4630 〈cop 4636 ∪ ciun 4997 ‘cfv 6549 predc-bnj14 34450 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 ax-sep 5300 ax-nul 5307 ax-pr 5429 ax-un 7741 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-v 3463 df-dif 3947 df-un 3949 df-ss 3961 df-nul 4323 df-sn 4631 df-pr 4633 df-uni 4910 |
This theorem is referenced by: bnj600 34681 bnj908 34693 |
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