Theorem difeq2i 3191

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 3188	. 2 |- ( A = B -> ( C \ A ) = ( C \ B ) )
3	1, 2	ax-mp 5	1 |- ( C \ A ) = ( C \ B )

Syntax hints:   = wceq 1331   \ cdif 3068

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 603  ax-in2 604  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-ral 2421  df-rab 2425  df-dif 3073

This theorem is referenced by:  difeq12i  3192  inssddif  3317  difdif2ss  3333  dif32  3339  difabs  3340  symdif1  3341  notrab  3353  dif0  3433  difdifdirss  3447  dfif3  3487  difpr  3662  dif1o  6335  unfiin  6814