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Mirrors > Home > ILE Home > Th. List > repizf2lem | Unicode version |
Description: Lemma for repizf2 3915. If we have a function-like proposition
which
provides at most one value of ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
repizf2lem |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mo 1904 |
. . . 4
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2 | 1 | imbi2i 215 |
. . 3
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3 | 2 | albii 1359 |
. 2
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4 | df-ral 2311 |
. 2
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5 | df-ral 2311 |
. . 3
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6 | rabid 2485 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | imbi1i 227 |
. . . . 5
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8 | impexp 250 |
. . . . 5
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9 | 7, 8 | bitri 173 |
. . . 4
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10 | 9 | albii 1359 |
. . 3
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11 | 5, 10 | bitri 173 |
. 2
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12 | 3, 4, 11 | 3bitr4i 201 |
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-8 1395 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-sb 1646 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-ral 2311 df-rab 2315 |
This theorem is referenced by: repizf2 3915 |
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