Theorem bcxmaslem1 11631

Description: Lemma for bcxmas 11632. (Contributed by Paul Chapman, 18-May-2007.)

Assertion

Ref	Expression
bcxmaslem1	|- ( A = B -> ( ( N + A ) _C A ) = ( ( N + B ) _C B ) )

Proof of Theorem bcxmaslem1

Step	Hyp	Ref	Expression
1		oveq2 5926	. 2 |- ( A = B -> ( N + A ) = ( N + B ) )
2		id 19	. 2 |- ( A = B -> A = B )
3	1, 2	oveq12d 5936	1 |- ( A = B -> ( ( N + A ) _C A ) = ( ( N + B ) _C B ) )

Syntax hints:   -> wi 4   = wceq 1364  (class class class)co 5918   + caddc 7875   _C cbc 10818

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-rex 2478  df-v 2762  df-un 3157  df-sn 3624  df-pr 3625  df-op 3627  df-uni 3836  df-br 4030  df-iota 5215  df-fv 5262  df-ov 5921

This theorem is referenced by:  bcxmas  11632