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Mirrors > Home > ILE Home > Th. List > repizf2lem | Unicode version |
Description: Lemma for repizf2 3906. If we have a function-like proposition
which
provides at most one value of ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
repizf2lem |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mo 1901 |
. . . 4
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2 | 1 | imbi2i 215 |
. . 3
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3 | 2 | albii 1356 |
. 2
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4 | df-ral 2305 |
. 2
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5 | df-ral 2305 |
. . 3
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6 | rabid 2479 |
. . . . . 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 1356 |
. . 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 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-sb 1643 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-ral 2305 df-rab 2309 |
This theorem is referenced by: repizf2 3906 |
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