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Theorem 4atex2-0cOLDN 30891
 Description: Same as 4atex2 30888 except that and are zero. TODO: do we need this one or 4atex2-0aOLDN 30889 or 4atex2-0bOLDN 30890? (Contributed by NM, 27-May-2013.) (New usage is discouraged.)
Hypotheses
Ref Expression
4that.l
4that.j
4that.a
4that.h
Assertion
Ref Expression
4atex2-0cOLDN
Distinct variable groups:   ,,   ,   ,,   ,,   ,,   ,,   ,,   ,,   ,,   ,,   ,

Proof of Theorem 4atex2-0cOLDN
StepHypRef Expression
1 simp21l 1072 . 2
2 simp21r 1073 . 2
3 simp23 990 . . . 4
43oveq1d 5889 . . 3
5 simp32 992 . . . 4
65oveq1d 5889 . . 3
74, 6eqtr4d 2331 . 2
8 breq1 4042 . . . . 5
98notbid 285 . . . 4
10 oveq2 5882 . . . . 5
11 oveq2 5882 . . . . 5
1210, 11eqeq12d 2310 . . . 4
139, 12anbi12d 691 . . 3
1413rspcev 2897 . 2
151, 2, 7, 14syl12anc 1180 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358   w3a 934   wceq 1632   wcel 1696   wne 2459  wrex 2557   class class class wbr 4039  cfv 5271  (class class class)co 5874  cple 13231  cjn 14094  cp0 14159  catm 30075  chlt 30162  clh 30795 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877
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