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Theorem csbeq2dv 2903
Description: Formula-building deduction rule for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)
Hypothesis
Ref Expression
csbeq2dv.1 (𝜑𝐵 = 𝐶)
Assertion
Ref Expression
csbeq2dv (𝜑𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶)
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝐴(𝑥)   𝐵(𝑥)   𝐶(𝑥)

Proof of Theorem csbeq2dv
StepHypRef Expression
1 nfv 1437 . 2 𝑥𝜑
2 csbeq2dv.1 . 2 (𝜑𝐵 = 𝐶)
31, 2csbeq2d 2902 1 (𝜑𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1259  csb 2880
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-sbc 2788  df-csb 2881
This theorem is referenced by:  csbeq2i  2904  mpt2mptsx  5851  dmmpt2ssx  5853  fmpt2x  5854  fmpt2co  5865
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