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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2027 | . . . 4 | |
2 | nfeu1 2008 | . . . . . 6 | |
3 | nfv 1508 | . . . . . 6 | |
4 | 2, 3 | nfim 1551 | . . . . 5 |
5 | tz6.12-1 5441 | . . . . . . . 8 | |
6 | 5 | expcom 115 | . . . . . . 7 |
7 | breq2 3928 | . . . . . . . 8 | |
8 | 7 | biimprd 157 | . . . . . . 7 |
9 | 6, 8 | syli 37 | . . . . . 6 |
10 | 9 | com12 30 | . . . . 5 |
11 | 4, 10 | exlimi 1573 | . . . 4 |
12 | 1, 11 | mpcom 36 | . . 3 |
13 | 12, 7 | syl5ibcom 154 | . 2 |
14 | 13, 6 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 wex 1468 weu 1997 class class class wbr 3924 cfv 5118 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 df-sbc 2905 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 |
This theorem is referenced by: fnbrfvb 5455 |
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