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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 2049 | . . . 4 | |
2 | nfeu1 2030 | . . . . . 6 | |
3 | nfv 1521 | . . . . . 6 | |
4 | 2, 3 | nfim 1565 | . . . . 5 |
5 | tz6.12-1 5521 | . . . . . . . 8 | |
6 | 5 | expcom 115 | . . . . . . 7 |
7 | breq2 3991 | . . . . . . . 8 | |
8 | 7 | biimprd 157 | . . . . . . 7 |
9 | 6, 8 | syli 37 | . . . . . 6 |
10 | 9 | com12 30 | . . . . 5 |
11 | 4, 10 | exlimi 1587 | . . . 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 1348 wex 1485 weu 2019 class class class wbr 3987 cfv 5196 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-sbc 2956 df-un 3125 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-iota 5158 df-fv 5204 |
This theorem is referenced by: fnbrfvb 5535 |
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