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Theorem csbeq1d 3013
Description: Equality deduction for proper substitution into a class. (Contributed by NM, 3-Dec-2005.)
Hypothesis
Ref Expression
csbeq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
csbeq1d (𝜑𝐴 / 𝑥𝐶 = 𝐵 / 𝑥𝐶)

Proof of Theorem csbeq1d
StepHypRef Expression
1 csbeq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 csbeq1 3009 . 2 (𝐴 = 𝐵𝐴 / 𝑥𝐶 = 𝐵 / 𝑥𝐶)
31, 2syl 14 1 (𝜑𝐴 / 𝑥𝐶 = 𝐵 / 𝑥𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1332  csb 3006
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-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-sbc 2913  df-csb 3007
This theorem is referenced by:  csbidmg  3060  csbco3g  3062  fmptcof  5594  mpomptsx  6102  dmmpossx  6104  fmpox  6105  fmpoco  6120  xpf1o  6745  summodclem3  11180  summodclem2a  11181  summodc  11183  zsumdc  11184  fsum3  11187  sumsnf  11209  fsumcnv  11237  fisumcom2  11238  fsumshftm  11245  fisum0diag2  11247  prodmodclem3  11375  prodmodclem2a  11376  prodmodc  11378  zproddc  11379  ctiunctlemu1st  11981  ctiunctlemu2nd  11982  ctiunctlemudc  11984  ctiunctlemfo  11986
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