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Theorem csbeq1d 2852
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 2849 . 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 1242  csb 2846
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-sbc 2759  df-csb 2847
This theorem is referenced by:  csbidmg  2896  csbco3g  2898  fmptcof  5274  mpt2mptsx  5765  dmmpt2ssx  5767  fmpt2x  5768  fmpt2co  5779
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