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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alcom 1412 |
. . 3
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2 | hbnae 1656 |
. . . 4
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3 | dveeq1 1943 |
. . . . . . 7
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4 | 3 | alimi 1389 |
. . . . . 6
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5 | 4 | hbnaes 1658 |
. . . . 5
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6 | 19.21ht 1518 |
. . . . 5
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7 | 5, 6 | syl 14 |
. . . 4
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8 | 2, 7 | albidh 1414 |
. . 3
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9 | 1, 8 | syl5rbbr 193 |
. 2
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10 | sb6 1814 |
. 2
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11 | sb6 1814 |
. . 3
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12 | 11 | albii 1404 |
. 2
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13 | 9, 10, 12 | 3bitr4g 221 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 |
This theorem is referenced by: (None) |
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