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Mirrors > Home > ILE Home > Th. List > tz6.12c | Unicode version |
Description: Corollary of Theorem 6.12(1) of [TakeutiZaring] p. 27. (Contributed by NM, 30-Apr-2004.) |
Ref | Expression |
---|---|
tz6.12c |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 1978 |
. . . 4
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2 | nfeu1 1959 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | nfv 1466 |
. . . . . 6
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4 | 2, 3 | nfim 1509 |
. . . . 5
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5 | tz6.12-1 5331 |
. . . . . . . 8
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6 | 5 | expcom 114 |
. . . . . . 7
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7 | breq2 3849 |
. . . . . . . 8
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8 | 7 | biimprd 156 |
. . . . . . 7
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9 | 6, 8 | syli 37 |
. . . . . 6
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10 | 9 | com12 30 |
. . . . 5
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11 | 4, 10 | exlimi 1530 |
. . . 4
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12 | 1, 11 | mpcom 36 |
. . 3
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13 | 12, 7 | syl5ibcom 153 |
. 2
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14 | 13, 6 | impbid 127 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-eu 1951 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rex 2365 df-v 2621 df-sbc 2841 df-un 3003 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-br 3846 df-iota 4980 df-fv 5023 |
This theorem is referenced by: fnbrfvb 5345 |
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