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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj95 | Structured version Visualization version GIF version |
Description: Technical lemma for bnj124 32042. 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 5322 | . 2 ⊢ {〈∅, pred(𝑥, 𝐴, 𝑅)〉} ∈ V | |
3 | 1, 2 | eqeltri 2906 | 1 ⊢ 𝐹 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ∈ wcel 2105 Vcvv 3492 ∅c0 4288 {csn 4557 〈cop 4563 predc-bnj14 31857 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pr 5320 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-v 3494 df-dif 3936 df-un 3938 df-nul 4289 df-sn 4558 df-pr 4560 |
This theorem is referenced by: bnj124 32042 bnj125 32043 bnj126 32044 bnj150 32047 |
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