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Mirrors > Home > NFE Home > Th. List > hbn1fw | Unicode version |
Description: Weak version of ax-6 1729 from which we can prove any ax-6 1729 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 19-Apr-2017.) |
Ref | Expression |
---|---|
hbn1fw.1 |
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hbn1fw.2 |
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hbn1fw.3 |
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hbn1fw.4 |
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hbn1fw.5 |
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hbn1fw.6 |
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Ref | Expression |
---|---|
hbn1fw |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbn1fw.1 |
. . . . 5
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2 | hbn1fw.2 |
. . . . 5
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3 | hbn1fw.3 |
. . . . 5
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4 | hbn1fw.4 |
. . . . 5
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5 | hbn1fw.6 |
. . . . 5
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6 | 1, 2, 3, 4, 5 | cbvalw 1701 |
. . . 4
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7 | 6 | biimpri 197 |
. . 3
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8 | 7 | con3i 127 |
. 2
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9 | hbn1fw.5 |
. 2
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10 | 6 | biimpi 186 |
. . . 4
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11 | 10 | con3i 127 |
. . 3
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12 | 11 | alimi 1559 |
. 2
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13 | 8, 9, 12 | 3syl 18 |
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 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 |
This theorem is referenced by: hbn1w 1706 |
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