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Mirrors > Home > ILE Home > Th. List > Mathboxes > if0ab | Unicode version |
Description: Expression of a
conditional class as a class abstraction when the False
alternative is the empty class: in that case, the conditional class is
the extension, in the True alternative, of the condition.
Remark: a consequence which could be formalized is the inclusion
|
Ref | Expression |
---|---|
if0ab |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3426 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() | |
2 | 1 | intnanr 930 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | 2 | biorfi 746 |
. . . 4
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4 | 3 | bicomi 132 |
. . 3
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5 | 4 | abbii 2293 |
. 2
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6 | df-if 3535 |
. 2
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7 | df-rab 2464 |
. 2
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8 | 5, 6, 7 | 3eqtr4i 2208 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rab 2464 df-v 2739 df-dif 3131 df-nul 3423 df-if 3535 |
This theorem is referenced by: (None) |
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