MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  bcxmaslem1 Structured version   Visualization version   GIF version

Theorem bcxmaslem1 14904
Description: Lemma for bcxmas 14905. (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 6886 . 2 (𝐴 = 𝐵 → (𝑁 + 𝐴) = (𝑁 + 𝐵))
2 id 22 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2oveq12d 6896 1 (𝐴 = 𝐵 → ((𝑁 + 𝐴)C𝐴) = ((𝑁 + 𝐵)C𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1653  (class class class)co 6878   + caddc 10227  Ccbc 13342
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2777
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-3an 1110  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-rex 3095  df-rab 3098  df-v 3387  df-dif 3772  df-un 3774  df-in 3776  df-ss 3783  df-nul 4116  df-if 4278  df-sn 4369  df-pr 4371  df-op 4375  df-uni 4629  df-br 4844  df-iota 6064  df-fv 6109  df-ov 6881
This theorem is referenced by:  bcxmas  14905  sylow1lem1  18326
  Copyright terms: Public domain W3C validator