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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 1586 |
. 2
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2 | 19.29r 1512 |
. . 3
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3 | hba1 1433 |
. . . . 5
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4 | pm3.35 329 |
. . . . 5
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5 | 3, 4 | exlimih 1484 |
. . . 4
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6 | ax-4 1400 |
. . . 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 400 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: equsalh 1614 spimth 1623 spimh 1625 |
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