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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj95 | Structured version Visualization version GIF version |
Description: Technical lemma for bnj124 32564. 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 5324 | . 2 ⊢ {〈∅, pred(𝑥, 𝐴, 𝑅)〉} ∈ V | |
3 | 1, 2 | eqeltri 2834 | 1 ⊢ 𝐹 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1543 ∈ wcel 2110 Vcvv 3408 ∅c0 4237 {csn 4541 〈cop 4547 predc-bnj14 32379 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-ext 2708 ax-sep 5192 ax-nul 5199 ax-pr 5322 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-tru 1546 df-fal 1556 df-ex 1788 df-sb 2071 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3410 df-dif 3869 df-un 3871 df-nul 4238 df-sn 4542 df-pr 4544 |
This theorem is referenced by: bnj124 32564 bnj125 32565 bnj126 32566 bnj150 32569 |
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