Mathbox for Rohan Ridenour |
< Previous
Next >
Nearby theorems |
||
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 40662 | . 2 ⊢ (𝐹 Coll 𝐴) = ∪ 𝑦 ∈ 𝐴 Scott (𝐹 “ {𝑦}) | |
2 | nfcoll.2 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | nfcoll.1 | . . . . 5 ⊢ Ⅎ𝑥𝐹 | |
4 | nfcv 2976 | . . . . 5 ⊢ Ⅎ𝑥{𝑦} | |
5 | 3, 4 | nfima 5930 | . . . 4 ⊢ Ⅎ𝑥(𝐹 “ {𝑦}) |
6 | 5 | nfscott 40650 | . . 3 ⊢ Ⅎ𝑥Scott (𝐹 “ {𝑦}) |
7 | 2, 6 | nfiun 4942 | . 2 ⊢ Ⅎ𝑥∪ 𝑦 ∈ 𝐴 Scott (𝐹 “ {𝑦}) |
8 | 1, 7 | nfcxfr 2974 | 1 ⊢ Ⅎ𝑥(𝐹 Coll 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2960 {csn 4560 ∪ ciun 4912 “ cima 5551 Scott cscott 40646 Coll ccoll 40661 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2792 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1084 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-clab 2799 df-cleq 2813 df-clel 2892 df-nfc 2962 df-ral 3142 df-rex 3143 df-rab 3146 df-v 3493 df-dif 3932 df-un 3934 df-in 3936 df-ss 3945 df-nul 4285 df-if 4461 df-sn 4561 df-pr 4563 df-op 4567 df-iun 4914 df-br 5060 df-opab 5122 df-xp 5554 df-cnv 5556 df-dm 5558 df-rn 5559 df-res 5560 df-ima 5561 df-scott 40647 df-coll 40662 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |