Theorem difeq1i 3103

Description: Inference adding difference to the right in a class equality. (Contributed by NM, 15-Nov-2002.)

Hypothesis

Ref	Expression
difeq1i.1	|- A = B

Assertion

Ref	Expression
difeq1i	|- ( A \ C ) = ( B \ C )

Proof of Theorem difeq1i

Step	Hyp	Ref	Expression
1		difeq1i.1	. 2 |- A = B
2		difeq1 3100	. 2 |- ( A = B -> ( A \ C ) = ( B \ C ) )
3	1, 2	ax-mp 7	1 |- ( A \ C ) = ( B \ C )

Syntax hints:   = wceq 1287   \ cdif 2985

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067

This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rab 2364  df-dif 2990

This theorem is referenced by:  difeq12i  3105  indif1  3233  indifcom  3234  difun1  3248  notab  3258  notrab  3265  difprsn1  3561  difprsn2  3562  orddif  4338  resdmdfsn  4724  phplem1  6522  dfn2  8622