Theorem difeq1i 2155

Description: Inference adding difference to the right in a class equality.

Hypothesis

Ref	Expression
difeq1i.1	|- A = B

Assertion

Ref	Expression
difeq1i	|- (A \ C) = (B \ C)

Proof of Theorem difeq1i

Step	Hyp	Ref	Expression
1		difeq1i.1	. 2 |- A = B
2		difeq1 2153	. 2 |- (A = B -> (A \ C) = (B \ C))
3	1, 2	ax-mp 7	1 |- (A \ C) = (B \ C)

Syntax hints:   = wceq 956   \ cdif 2044

This theorem is referenced by:  difeq12i 2157  dfin3 2247  difun1 2263  orddif 3075  phplem1 4508

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-dif 2049

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