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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj95 | Structured version Visualization version GIF version | ||
| Description: Technical lemma for bnj124 34885. 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 5436 | . 2 ⊢ {〈∅, pred(𝑥, 𝐴, 𝑅)〉} ∈ V | |
| 3 | 1, 2 | eqeltri 2837 | 1 ⊢ 𝐹 ∈ V | 
| Colors of variables: wff setvar class | 
| Syntax hints: = wceq 1540 ∈ wcel 2108 Vcvv 3480 ∅c0 4333 {csn 4626 〈cop 4632 predc-bnj14 34702 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pr 5432 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-dif 3954 df-un 3956 df-nul 4334 df-sn 4627 df-pr 4629 | 
| This theorem is referenced by: bnj124 34885 bnj125 34886 bnj126 34887 bnj150 34890 | 
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