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Mirrors > Home > NFE Home > Th. List > 19.33b | Unicode version |
Description: The antecedent provides a condition implying the converse of 19.33 1607. Compare Theorem 19.33 of [Margaris] p. 90. (Contributed by NM, 27-Mar-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 5-Jul-2014.) |
Ref | Expression |
---|---|
19.33b |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ianor 474 |
. . 3
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2 | alnex 1543 |
. . . . . 6
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3 | pm2.53 362 |
. . . . . . 7
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4 | 3 | al2imi 1561 |
. . . . . 6
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5 | 2, 4 | syl5bir 209 |
. . . . 5
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6 | olc 373 |
. . . . 5
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7 | 5, 6 | syl6com 31 |
. . . 4
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8 | 19.30 1604 |
. . . . . . 7
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9 | 8 | orcomd 377 |
. . . . . 6
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10 | 9 | ord 366 |
. . . . 5
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11 | orc 374 |
. . . . 5
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12 | 10, 11 | syl6com 31 |
. . . 4
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13 | 7, 12 | jaoi 368 |
. . 3
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14 | 1, 13 | sylbi 187 |
. 2
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15 | 19.33 1607 |
. 2
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16 | 14, 15 | impbid1 194 |
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 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-ex 1542 |
This theorem is referenced by: (None) |
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