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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj95 | Structured version Visualization version GIF version |
Description: Technical lemma for bnj124 34502. 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 |
---|---|
bnj95.1 | ⊢ 𝐹 = {⟨∅, pred(𝑥, 𝐴, 𝑅)⟩} |
Ref | Expression |
---|---|
bnj95 | ⊢ 𝐹 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj95.1 | . 2 ⊢ 𝐹 = {⟨∅, pred(𝑥, 𝐴, 𝑅)⟩} | |
2 | snex 5433 | . 2 ⊢ {⟨∅, pred(𝑥, 𝐴, 𝑅)⟩} ∈ V | |
3 | 1, 2 | eqeltri 2825 | 1 ⊢ 𝐹 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1534 ∈ wcel 2099 Vcvv 3471 ∅c0 4323 {csn 4629 ⟨cop 4635 predc-bnj14 34319 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2699 ax-sep 5299 ax-nul 5306 ax-pr 5429 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2706 df-cleq 2720 df-clel 2806 df-v 3473 df-dif 3950 df-un 3952 df-nul 4324 df-sn 4630 df-pr 4632 |
This theorem is referenced by: bnj124 34502 bnj125 34503 bnj126 34504 bnj150 34507 |
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