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Mirrors > Home > NFE 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 1737 |
. . 3
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2 | nfnae 1956 |
. . . 4
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3 | nfnae 1956 |
. . . . . 6
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4 | dveeq1 2018 |
. . . . . 6
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5 | 3, 4 | nfd 1766 |
. . . . 5
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6 | 19.21t 1795 |
. . . . 5
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7 | 5, 6 | syl 15 |
. . . 4
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8 | 2, 7 | albid 1772 |
. . 3
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9 | 1, 8 | syl5rbbr 251 |
. 2
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10 | sb6 2099 |
. 2
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11 | sb6 2099 |
. . 3
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12 | 11 | albii 1566 |
. 2
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13 | 9, 10, 12 | 3bitr4g 279 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 |
This theorem is referenced by: (None) |
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