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Theorem acongeq12d 27169
 Description: Substitution deduction for alternating congruence. (Contributed by Stefan O'Rear, 3-Oct-2014.)
Hypotheses
Ref Expression
acongeq12d.1
acongeq12d.2
Assertion
Ref Expression
acongeq12d

Proof of Theorem acongeq12d
StepHypRef Expression
1 acongeq12d.1 . . . 4
2 acongeq12d.2 . . . 4
31, 2oveq12d 5892 . . 3
43breq2d 4051 . 2
52negeqd 9062 . . . 4
61, 5oveq12d 5892 . . 3
76breq2d 4051 . 2
84, 7orbi12d 690 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wo 357   wceq 1632   class class class wbr 4039  (class class class)co 5874   cmin 9053  cneg 9054   cdivides 12547 This theorem is referenced by:  acongrep  27170  jm2.26a  27196  jm2.26  27198 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  df-neg 9056
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