Theorem difeq12i 3114

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 3112	. 2 |- ( A \ C ) = ( B \ C )
3		difeq12i.2	. . 3 |- C = D
4	3	difeq2i 3113	. 2 |- ( B \ C ) = ( B \ D )
5	2, 4	eqtri 2108	1 |- ( A \ C ) = ( B \ D )

Syntax hints:   = wceq 1289   \ cdif 2994

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-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-rab 2368  df-dif 2999

This theorem is referenced by:  difrab  3271  imadiflem  5079  imadif  5080