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Mirrors > Home > NFE Home > Th. List > sb9i | Unicode version |
Description: Commutation of quantification and substitution variables. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sb9i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | drsb1 2022 |
. . . . 5
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2 | drsb2 2061 |
. . . . 5
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3 | 1, 2 | bitr3d 246 |
. . . 4
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4 | 3 | dral1 1965 |
. . 3
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5 | 4 | biimprd 214 |
. 2
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6 | nfnae 1956 |
. . . 4
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7 | hbsb2 2057 |
. . . 4
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8 | 6, 7 | alimd 1764 |
. . 3
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9 | stdpc4 2024 |
. . . . . 6
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10 | sbco 2083 |
. . . . . 6
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11 | 9, 10 | sylib 188 |
. . . . 5
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12 | 11 | alimi 1559 |
. . . 4
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13 | 12 | a7s 1735 |
. . 3
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14 | 8, 13 | syl6 29 |
. 2
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15 | 5, 14 | pm2.61i 156 |
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-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 |
This theorem is referenced by: sb9 2095 |
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