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Theorem bcxmaslem1 11451
Description: Lemma for bcxmas 11452. (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 5861 . 2 (𝐴 = 𝐵 → (𝑁 + 𝐴) = (𝑁 + 𝐵))
2 id 19 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2oveq12d 5871 1 (𝐴 = 𝐵 → ((𝑁 + 𝐴)C𝐴) = ((𝑁 + 𝐵)C𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1348  (class class class)co 5853   + caddc 7777  Ccbc 10681
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-v 2732  df-un 3125  df-sn 3589  df-pr 3590  df-op 3592  df-uni 3797  df-br 3990  df-iota 5160  df-fv 5206  df-ov 5856
This theorem is referenced by:  bcxmas  11452
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