Theorem difeq12i 2155

Description: Equality inference for class difference.

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 2153	. 2 |- (A \ C) = (B \ C)
3		difeq12i.2	. . 3 |- C = D
4	3	difeq2i 2154	. 2 |- (B \ C) = (B \ D)
5	2, 4	eqtr 1494	1 |- (A \ C) = (B \ D)

Syntax hints:   = wceq 955   \ cdif 2042

This theorem is referenced by:  difrab 2271

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-dif 2047

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