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Mirrors > Home > NFE Home > Th. List > rblem5 | Unicode version |
Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 19-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
rblem5 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rb-ax2 1518 |
. 2
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2 | rb-ax4 1520 |
. . . . 5
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3 | rb-ax3 1519 |
. . . . 5
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4 | 2, 3 | rbsyl 1521 |
. . . 4
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5 | rb-ax4 1520 |
. . . . . . 7
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6 | rb-ax3 1519 |
. . . . . . 7
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7 | 5, 6 | rbsyl 1521 |
. . . . . 6
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8 | rb-ax2 1518 |
. . . . . 6
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9 | 7, 8 | anmp 1516 |
. . . . 5
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10 | 9, 4 | rblem1 1522 |
. . . 4
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11 | 4, 10 | anmp 1516 |
. . 3
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12 | rb-ax4 1520 |
. . . . 5
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13 | rb-ax3 1519 |
. . . . 5
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14 | 12, 13 | rbsyl 1521 |
. . . 4
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15 | rb-ax2 1518 |
. . . 4
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16 | 14, 15 | anmp 1516 |
. . 3
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17 | 11, 16 | rblem1 1522 |
. 2
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18 | 1, 17 | rbsyl 1521 |
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 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 |
This theorem is referenced by: rblem6 1527 rblem7 1528 |
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