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Theorem tz6.12c 5417
 Description: Corollary of Theorem 6.12(1) of [TakeutiZaring] p. 27. (Contributed by NM, 30-Apr-2004.)
Assertion
Ref Expression
tz6.12c
Distinct variable groups:   ,   ,

Proof of Theorem tz6.12c
StepHypRef Expression
1 euex 2005 . . . 4
2 nfeu1 1986 . . . . . 6
3 nfv 1491 . . . . . 6
42, 3nfim 1534 . . . . 5
5 tz6.12-1 5414 . . . . . . . 8
65expcom 115 . . . . . . 7
7 breq2 3901 . . . . . . . 8
87biimprd 157 . . . . . . 7
96, 8syli 37 . . . . . 6
109com12 30 . . . . 5
114, 10exlimi 1556 . . . 4
121, 11mpcom 36 . . 3
1312, 7syl5ibcom 154 . 2
1413, 6impbid 128 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1314  wex 1451  weu 1975   class class class wbr 3897  cfv 5091 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-sbc 2881  df-un 3043  df-sn 3501  df-pr 3502  df-op 3504  df-uni 3705  df-br 3898  df-iota 5056  df-fv 5099 This theorem is referenced by:  fnbrfvb  5428
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