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Mirrors > Home > ILE Home > Th. List > nfcsbw | Unicode version |
Description: Bound-variable hypothesis builder for substitution into a class. Version of nfcsb 3068 with a disjoint variable condition. (Contributed by Mario Carneiro, 12-Oct-2016.) (Revised by Gino Giotto, 10-Jan-2024.) |
Ref | Expression |
---|---|
nfcsbw.1 | |
nfcsbw.2 |
Ref | Expression |
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nfcsbw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-csb 3032 | . . 3 | |
2 | nftru 1446 | . . . 4 | |
3 | nftru 1446 | . . . . 5 | |
4 | nfcsbw.1 | . . . . . 6 | |
5 | 4 | a1i 9 | . . . . 5 |
6 | nfcsbw.2 | . . . . . . 7 | |
7 | 6 | a1i 9 | . . . . . 6 |
8 | 7 | nfcrd 2313 | . . . . 5 |
9 | 3, 5, 8 | nfsbcdw 3065 | . . . 4 |
10 | 2, 9 | nfabdw 2318 | . . 3 |
11 | 1, 10 | nfcxfrd 2297 | . 2 |
12 | 11 | mptru 1344 | 1 |
Colors of variables: wff set class |
Syntax hints: wtru 1336 wcel 2128 cab 2143 wnfc 2286 wsbc 2937 csb 3031 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-sbc 2938 df-csb 3032 |
This theorem is referenced by: fprod2dlemstep 11512 fprodcom2fi 11516 |
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