Theorem difeq2d 3090

Description: Deduction adding difference to the left in a class equality. (Contributed by NM, 15-Nov-2002.)

Hypothesis

Ref	Expression
difeq1d.1	|- ( ph -> A = B )

Assertion

Ref	Expression
difeq2d	|- ( ph -> ( C \ A ) = ( C \ B ) )

Proof of Theorem difeq2d

Step	Hyp	Ref	Expression
1		difeq1d.1	. 2 |- ( ph -> A = B )
2		difeq2 3084	. 2 |- ( A = B -> ( C \ A ) = ( C \ B ) )
3	1, 2	syl 14	1 |- ( ph -> ( C \ A ) = ( C \ B ) )

Syntax hints:   -> wi 4   = wceq 1284   \ cdif 2970

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 576  ax-in2 577  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-ral 2353  df-rab 2357  df-dif 2975

This theorem is referenced by:  difeq12d  3091  phplem3  6340  phplem4  6341  phplem3g  6342  phplem4dom  6348  phplem4on  6353  fidifsnen  6355