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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 31487. 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 5129 | . 2 ⊢ {〈∅, pred(𝑥, 𝐴, 𝑅)〉} ∈ V | |
3 | 1, 2 | eqeltri 2902 | 1 ⊢ 𝐹 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1658 ∈ wcel 2166 Vcvv 3414 ∅c0 4144 {csn 4397 〈cop 4403 predc-bnj14 31303 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-9 2175 ax-10 2194 ax-11 2209 ax-12 2222 ax-13 2391 ax-ext 2803 ax-sep 5005 ax-nul 5013 ax-pr 5127 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-tru 1662 df-ex 1881 df-nf 1885 df-sb 2070 df-clab 2812 df-cleq 2818 df-clel 2821 df-nfc 2958 df-v 3416 df-dif 3801 df-un 3803 df-nul 4145 df-sn 4398 df-pr 4400 |
This theorem is referenced by: bnj124 31487 bnj125 31488 bnj126 31489 bnj150 31492 |
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