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Mirrors > Home > ILE Home > Th. List > sbal2 | Unicode version |
Description: Move quantifier in and out of substitution. (Contributed by NM, 2-Jan-2002.) |
Ref | Expression |
---|---|
sbal2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbnae 1701 | . . . 4 | |
2 | dveeq1 1999 | . . . . . . 7 | |
3 | 2 | alimi 1435 | . . . . . 6 |
4 | 3 | hbnaes 1703 | . . . . 5 |
5 | 19.21ht 1561 | . . . . 5 | |
6 | 4, 5 | syl 14 | . . . 4 |
7 | 1, 6 | albidh 1460 | . . 3 |
8 | alcom 1458 | . . 3 | |
9 | 7, 8 | bitr3di 194 | . 2 |
10 | sb6 1866 | . 2 | |
11 | sb6 1866 | . . 3 | |
12 | 11 | albii 1450 | . 2 |
13 | 9, 10, 12 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wal 1333 wsb 1742 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 |
This theorem is referenced by: (None) |
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