Theorem difeq2i 3242

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

Hypothesis

Ref	Expression
difeq1i.1	|- A = B

Assertion

Ref	Expression
difeq2i	|- ( C \ A ) = ( C \ B )

Proof of Theorem difeq2i

Step	Hyp	Ref	Expression
1		difeq1i.1	. 2 |- A = B
2		difeq2 3239	. 2 |- ( A = B -> ( C \ A ) = ( C \ B ) )
3	1, 2	ax-mp 5	1 |- ( C \ A ) = ( C \ B )

Syntax hints:   = wceq 1348   \ cdif 3118

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-in1 609  ax-in2 610  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  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-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-ral 2453  df-rab 2457  df-dif 3123

This theorem is referenced by:  difeq12i  3243  inssddif  3368  difdif2ss  3384  dif32  3390  difabs  3391  symdif1  3392  notrab  3404  dif0  3485  difdifdirss  3499  dfif3  3539  difpr  3722  dif1o  6417  unfiin  6903