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Theorem csbeq1d 3142
 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 (φ[A / x]C = [B / x]C)

Proof of Theorem csbeq1d
StepHypRef Expression
1 csbeq1d.1 . 2 (φA = B)
2 csbeq1 3139 . 2 (A = B[A / x]C = [B / x]C)
31, 2syl 15 1 (φ[A / x]C = [B / x]C)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  [csb 3136 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-sbc 3047  df-csb 3137 This theorem is referenced by:  csbidmg  3190  csbco3g  3193  fmpt2x  5730
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