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Theorem bcxmaslem1 15179
Description: Lemma for bcxmas 15180. (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 7156 . 2 (𝐴 = 𝐵 → (𝑁 + 𝐴) = (𝑁 + 𝐵))
2 id 22 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2oveq12d 7166 1 (𝐴 = 𝐵 → ((𝑁 + 𝐴)C𝐴) = ((𝑁 + 𝐵)C𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1530  (class class class)co 7148   + caddc 10529  Ccbc 13652
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 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-rex 3149  df-rab 3152  df-v 3502  df-dif 3943  df-un 3945  df-in 3947  df-ss 3956  df-nul 4296  df-if 4471  df-sn 4565  df-pr 4567  df-op 4571  df-uni 4838  df-br 5064  df-iota 6312  df-fv 6360  df-ov 7151
This theorem is referenced by:  bcxmas  15180  sylow1lem1  18643
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