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Theorem bcxmaslem1 15237
 Description: Lemma for bcxmas 15238. (Contributed by Paul Chapman, 18-May-2007.)
Assertion
Ref Expression
bcxmaslem1 (𝐴 = 𝐵 → ((𝑁 + 𝐴)C𝐴) = ((𝑁 + 𝐵)C𝐵))

Proof of Theorem bcxmaslem1
StepHypRef Expression
1 oveq2 7158 . 2 (𝐴 = 𝐵 → (𝑁 + 𝐴) = (𝑁 + 𝐵))
2 id 22 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2oveq12d 7168 1 (𝐴 = 𝐵 → ((𝑁 + 𝐴)C𝐴) = ((𝑁 + 𝐵)C𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538  (class class class)co 7150   + caddc 10578  Ccbc 13712 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-v 3411  df-un 3863  df-in 3865  df-ss 3875  df-sn 4523  df-pr 4525  df-op 4529  df-uni 4799  df-br 5033  df-iota 6294  df-fv 6343  df-ov 7153 This theorem is referenced by:  bcxmas  15238  sylow1lem1  18790
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