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Theorem tz6.12c 5736
 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 2303 . . . 4
2 nfeu1 2290 . . . . . 6
3 nfv 1629 . . . . . 6
42, 3nfim 1832 . . . . 5
5 tz6.12-1 5733 . . . . . . . 8
65expcom 425 . . . . . . 7
7 breq2 4203 . . . . . . . 8
87biimprd 215 . . . . . . 7
96, 8syli 35 . . . . . 6
109com12 29 . . . . 5
114, 10exlimi 1821 . . . 4
121, 11mpcom 34 . . 3
1312, 7syl5ibcom 212 . 2
1413, 6impbid 184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wex 1550   wceq 1652  weu 2280   class class class wbr 4199  cfv 5440 This theorem is referenced by:  tz6.12i  5737  fnbrfvb  5753 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2411 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2417  df-cleq 2423  df-clel 2426  df-nfc 2555  df-rex 2698  df-rab 2701  df-v 2945  df-sbc 3149  df-dif 3310  df-un 3312  df-in 3314  df-ss 3321  df-nul 3616  df-if 3727  df-sn 3807  df-pr 3808  df-op 3810  df-uni 4003  df-br 4200  df-iota 5404  df-fv 5448
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