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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 31533. 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 31378 | 1 ⊢ 𝐺 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1656 ∈ wcel 2164 Vcvv 3414 ∪ cun 3796 {csn 4399 〈cop 4405 ∪ ciun 4742 ‘cfv 6127 predc-bnj14 31299 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-8 2166 ax-9 2173 ax-10 2192 ax-11 2207 ax-12 2220 ax-13 2389 ax-ext 2803 ax-sep 5007 ax-nul 5015 ax-pr 5129 ax-un 7214 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 879 df-tru 1660 df-ex 1879 df-nf 1883 df-sb 2068 df-clab 2812 df-cleq 2818 df-clel 2821 df-nfc 2958 df-rex 3123 df-v 3416 df-dif 3801 df-un 3803 df-nul 4147 df-sn 4400 df-pr 4402 df-uni 4661 |
This theorem is referenced by: bnj600 31531 bnj908 31543 |
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