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Theorem dmdi 23810
 Description: Consequence of the dual modular pair property. (Contributed by NM, 27-Apr-2006.) (New usage is discouraged.)
Assertion
Ref Expression
dmdi

Proof of Theorem dmdi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dmdbr 23807 . . . . 5
21biimpd 200 . . . 4
3 sseq2 3372 . . . . . 6
4 ineq1 3537 . . . . . . . 8
54oveq1d 6099 . . . . . . 7
6 ineq1 3537 . . . . . . 7
75, 6eqeq12d 2452 . . . . . 6
83, 7imbi12d 313 . . . . 5
98rspcv 3050 . . . 4
102, 9sylan9 640 . . 3
11103impa 1149 . 2
1211imp32 424 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937   wceq 1653   wcel 1726  wral 2707   cin 3321   wss 3322   class class class wbr 4215  (class class class)co 6084  cch 22437   chj 22441   cdmd 22475 This theorem is referenced by:  dmdi2  23812  dmdsl3  23823  csmdsymi  23842  mdsymlem1  23911 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-iota 5421  df-fv 5465  df-ov 6087  df-dmd 23789
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