Theorem difeq12i 3223

Description: Equality inference for class difference. (Contributed by NM, 29-Aug-2004.)

Hypotheses

Ref	Expression
difeq1i.1	|- A = B
difeq12i.2	|- C = D

Assertion

Ref	Expression
difeq12i	|- ( A \ C ) = ( B \ D )

Proof of Theorem difeq12i

Step	Hyp	Ref	Expression
1		difeq1i.1	. . 3 |- A = B
2	1	difeq1i 3221	. 2 |- ( A \ C ) = ( B \ C )
3		difeq12i.2	. . 3 |- C = D
4	3	difeq2i 3222	. 2 |- ( B \ C ) = ( B \ D )
5	2, 4	eqtri 2178	1 |- ( A \ C ) = ( B \ D )

Syntax hints:   = wceq 1335   \ cdif 3099

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 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rab 2444  df-dif 3104

This theorem is referenced by:  difrab  3381  imadiflem  5249  imadif  5250