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Mirrors > Home > NFE Home > Th. List > dvelimhw | Unicode version |
Description: Proof of dvelimh 1964 without using ax-12 1925 but with additional distinct variable conditions. (Contributed by Andrew Salmon, 21-Jul-2011.) (Revised by NM, 1-Aug-2017.) |
Ref | Expression |
---|---|
dvelimhw.1 |
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dvelimhw.2 |
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dvelimhw.3 |
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dvelimhw.4 |
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Ref | Expression |
---|---|
dvelimhw |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1616 |
. . 3
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2 | hbn1 1730 |
. . . 4
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3 | equcomi 1679 |
. . . . 5
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4 | dvelimhw.4 |
. . . . 5
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5 | equcomi 1679 |
. . . . . 6
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6 | 5 | alimi 1559 |
. . . . 5
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7 | 3, 4, 6 | syl56 30 |
. . . 4
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8 | dvelimhw.1 |
. . . . 5
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9 | 8 | a1i 10 |
. . . 4
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10 | 2, 7, 9 | hbimd 1815 |
. . 3
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11 | 1, 10 | hbald 1740 |
. 2
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12 | dvelimhw.2 |
. . 3
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13 | dvelimhw.3 |
. . 3
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14 | 12, 13 | equsalhw 1838 |
. 2
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15 | 14 | albii 1566 |
. 2
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16 | 11, 14, 15 | 3imtr3g 260 |
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 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-nf 1545 |
This theorem is referenced by: ax12olem6 1932 |
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