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Theorem bcxmaslem1 15812
Description: Lemma for bcxmas 15813. (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 7424 . 2 (𝐴 = 𝐵 → (𝑁 + 𝐴) = (𝑁 + 𝐵))
2 id 22 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2oveq12d 7434 1 (𝐴 = 𝐵 → ((𝑁 + 𝐴)C𝐴) = ((𝑁 + 𝐵)C𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  (class class class)co 7416   + caddc 11141  Ccbc 14293
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-rab 3420  df-v 3465  df-dif 3942  df-un 3944  df-ss 3956  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4904  df-br 5144  df-iota 6495  df-fv 6551  df-ov 7419
This theorem is referenced by:  bcxmas  15813  sylow1lem1  19557
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