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Mirrors > Home > ILE Home > Th. List > ax9o | Unicode version |
Description: An implication related to substitution. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.) |
Ref | Expression |
---|---|
ax9o |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1675 |
. 2
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2 | 19.29r 1601 |
. . 3
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3 | hba1 1521 |
. . . . 5
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4 | pm3.35 345 |
. . . . 5
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5 | 3, 4 | exlimih 1573 |
. . . 4
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6 | ax-4 1488 |
. . . 4
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7 | 5, 6 | syl 14 |
. . 3
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8 | 2, 7 | syl 14 |
. 2
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9 | 1, 8 | mpan 421 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-i9 1511 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: equsalh 1705 spimth 1714 spimh 1716 |
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