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Mirrors > Home > ILE Home > Th. List > sb9 | Unicode version |
Description: Commutation of quantification and substitution variables. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 23-Mar-2018.) |
Ref | Expression |
---|---|
sb9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb9v 1953 | . . 3 | |
2 | sbcom 1948 | . . . 4 | |
3 | 2 | albii 1446 | . . 3 |
4 | sb9v 1953 | . . 3 | |
5 | 1, 3, 4 | 3bitri 205 | . 2 |
6 | ax-17 1506 | . . . 4 | |
7 | 6 | sbco2h 1937 | . . 3 |
8 | 7 | albii 1446 | . 2 |
9 | 6 | sbco2h 1937 | . . 3 |
10 | 9 | albii 1446 | . 2 |
11 | 5, 8, 10 | 3bitr3ri 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1329 wsb 1735 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 |
This theorem is referenced by: sb9i 1955 |
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