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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 40677 | . 2 ⊢ (𝐹 Coll 𝐴) = ∪ 𝑦 ∈ 𝐴 Scott (𝐹 “ {𝑦}) | |
2 | nfcoll.2 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | nfcoll.1 | . . . . 5 ⊢ Ⅎ𝑥𝐹 | |
4 | nfcv 2977 | . . . . 5 ⊢ Ⅎ𝑥{𝑦} | |
5 | 3, 4 | nfima 5923 | . . . 4 ⊢ Ⅎ𝑥(𝐹 “ {𝑦}) |
6 | 5 | nfscott 40665 | . . 3 ⊢ Ⅎ𝑥Scott (𝐹 “ {𝑦}) |
7 | 2, 6 | nfiun 4935 | . 2 ⊢ Ⅎ𝑥∪ 𝑦 ∈ 𝐴 Scott (𝐹 “ {𝑦}) |
8 | 1, 7 | nfcxfr 2975 | 1 ⊢ Ⅎ𝑥(𝐹 Coll 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2961 {csn 4553 ∪ ciun 4905 “ cima 5544 Scott cscott 40661 Coll ccoll 40676 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-rab 3147 df-v 3488 df-dif 3927 df-un 3929 df-in 3931 df-ss 3940 df-nul 4280 df-if 4454 df-sn 4554 df-pr 4556 df-op 4560 df-iun 4907 df-br 5053 df-opab 5115 df-xp 5547 df-cnv 5549 df-dm 5551 df-rn 5552 df-res 5553 df-ima 5554 df-scott 40662 df-coll 40677 |
This theorem is referenced by: (None) |
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