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Theorem r19.2zb 3710
 Description: A response to the notion that the condition can be removed in r19.2z 3709. 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 3709 . . 3
21ex 424 . 2
3 noel 3624 . . . . . . 7
43pm2.21i 125 . . . . . 6
54rgen 2763 . . . . 5
6 raleq 2896 . . . . 5
75, 6mpbiri 225 . . . 4
87necon3bi 2639 . . 3
9 exsimpl 1602 . . . 4
10 df-rex 2703 . . . 4
11 n0 3629 . . . 4
129, 10, 113imtr4i 258 . . 3
138, 12ja 155 . 2
142, 13impbii 181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725   wne 2598  wral 2697  wrex 2698  c0 3620 This theorem is referenced by:  iinpreima  5852  utopbas  18255 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 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-nul 3621
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