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Mathbox for Rohan Ridenour |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > nfcoll | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for the collection operation. (Contributed by Rohan Ridenour, 11-Aug-2023.) |
Ref | Expression |
---|---|
nfcoll.1 | ⊢ Ⅎ𝑥𝐹 |
nfcoll.2 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfcoll | ⊢ Ⅎ𝑥(𝐹 Coll 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-coll 42881 | . 2 ⊢ (𝐹 Coll 𝐴) = ∪ 𝑦 ∈ 𝐴 Scott (𝐹 “ {𝑦}) | |
2 | nfcoll.2 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | nfcoll.1 | . . . . 5 ⊢ Ⅎ𝑥𝐹 | |
4 | nfcv 2904 | . . . . 5 ⊢ Ⅎ𝑥{𝑦} | |
5 | 3, 4 | nfima 6060 | . . . 4 ⊢ Ⅎ𝑥(𝐹 “ {𝑦}) |
6 | 5 | nfscott 42869 | . . 3 ⊢ Ⅎ𝑥Scott (𝐹 “ {𝑦}) |
7 | 2, 6 | nfiun 5023 | . 2 ⊢ Ⅎ𝑥∪ 𝑦 ∈ 𝐴 Scott (𝐹 “ {𝑦}) |
8 | 1, 7 | nfcxfr 2902 | 1 ⊢ Ⅎ𝑥(𝐹 Coll 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2884 {csn 4624 ∪ ciun 4993 “ cima 5675 Scott cscott 42865 Coll ccoll 42880 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ral 3063 df-rex 3072 df-rab 3434 df-v 3477 df-dif 3949 df-un 3951 df-in 3953 df-ss 3963 df-nul 4321 df-if 4525 df-sn 4625 df-pr 4627 df-op 4631 df-iun 4995 df-br 5145 df-opab 5207 df-xp 5678 df-cnv 5680 df-dm 5682 df-rn 5683 df-res 5684 df-ima 5685 df-scott 42866 df-coll 42881 |
This theorem is referenced by: (None) |
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