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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj528 | Structured version Visualization version GIF version |
Description: Technical lemma for bnj852 32909. 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 32754 | 1 ⊢ 𝐺 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1539 ∈ wcel 2106 Vcvv 3429 ∪ cun 3884 {csn 4561 〈cop 4567 ∪ ciun 4924 ‘cfv 6426 predc-bnj14 32675 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2709 ax-sep 5221 ax-nul 5228 ax-pr 5350 ax-un 7578 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-tru 1542 df-fal 1552 df-ex 1783 df-sb 2068 df-clab 2716 df-cleq 2730 df-clel 2816 df-v 3431 df-dif 3889 df-un 3891 df-in 3893 df-ss 3903 df-nul 4257 df-sn 4562 df-pr 4564 df-uni 4840 |
This theorem is referenced by: bnj600 32907 bnj908 32919 |
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