Theorem bcxmaslem1 15761

Description: Lemma for bcxmas 15762. (Contributed by Paul Chapman, 18-May-2007.)

Assertion

Ref	Expression
bcxmaslem1	⊢ (𝐴 = 𝐵 → ((𝑁 + 𝐴)C𝐴) = ((𝑁 + 𝐵)C𝐵))

Proof of Theorem bcxmaslem1

Step	Hyp	Ref	Expression
1		oveq2 7368	. 2 ⊢ (𝐴 = 𝐵 → (𝑁 + 𝐴) = (𝑁 + 𝐵))
2		id 22	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵)
3	1, 2	oveq12d 7378	1 ⊢ (𝐴 = 𝐵 → ((𝑁 + 𝐴)C𝐴) = ((𝑁 + 𝐵)C𝐵))

Syntax hints:   → wi 4   = wceq 1542  (class class class)co 7360   + caddc 11033  Ccbc 14229

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3401  df-v 3443  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4287  df-if 4481  df-sn 4582  df-pr 4584  df-op 4588  df-uni 4865  df-br 5100  df-iota 6449  df-fv 6501  df-ov 7363

This theorem is referenced by:  bcxmas  15762  sylow1lem1  19531