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Mirrors > Home > ILE Home > Th. List > opabbid | Unicode version |
Description: Equivalent wff's yield equal ordered-pair class abstractions (deduction form). (Contributed by NM, 21-Feb-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
opabbid.1 |
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opabbid.2 |
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opabbid.3 |
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Ref | Expression |
---|---|
opabbid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opabbid.1 |
. . . 4
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2 | opabbid.2 |
. . . . 5
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3 | opabbid.3 |
. . . . . 6
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4 | 3 | anbi2d 464 |
. . . . 5
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5 | 2, 4 | exbid 1627 |
. . . 4
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6 | 1, 5 | exbid 1627 |
. . 3
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7 | 6 | abbidv 2307 |
. 2
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8 | df-opab 4080 |
. 2
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9 | df-opab 4080 |
. 2
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10 | 7, 8, 9 | 3eqtr4g 2247 |
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-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-opab 4080 |
This theorem is referenced by: opabbidv 4084 mpteq12f 4098 fnoprabg 5997 |
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