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Theorem r19.2zb 3832
 Description: A response to the notion that the condition can be removed in r19.2z 3831. Interestingly enough, does not figure in the left-hand side. (Contributed by Jeff Hankins, 24-Aug-2009.)
Assertion
Ref Expression
r19.2zb
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem r19.2zb
StepHypRef Expression
1 r19.2z 3831 . . 3
21ex 435 . 2
3 noel 3708 . . . . . . 7
43pm2.21i 134 . . . . . 6
54rgen 2724 . . . . 5
6 raleq 2964 . . . . 5
75, 6mpbiri 236 . . . 4
87necon3bi 2627 . . 3
9 exsimpl 1723 . . . 4
10 df-rex 2720 . . . 4
11 n0 3714 . . . 4
129, 10, 113imtr4i 269 . . 3
138, 12ja 164 . 2
142, 13impbii 190 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437  wex 1657   wcel 1872   wne 2599  wral 2714  wrex 2715  c0 3704 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ne 2601  df-ral 2719  df-rex 2720  df-v 3024  df-dif 3382  df-nul 3705 This theorem is referenced by:  iinpreima  5969  utopbas  21192  radcnvrat  36576
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