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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 34914. 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 34759 | 1 ⊢ 𝐺 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ∈ wcel 2106 Vcvv 3478 ∪ cun 3961 {csn 4631 〈cop 4637 ∪ ciun 4996 ‘cfv 6563 predc-bnj14 34681 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 ax-sep 5302 ax-nul 5312 ax-pr 5438 ax-un 7754 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-fal 1550 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-v 3480 df-dif 3966 df-un 3968 df-ss 3980 df-nul 4340 df-sn 4632 df-pr 4634 df-uni 4913 |
This theorem is referenced by: bnj600 34912 bnj908 34924 |
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