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Theorem csbeq2i 3162
 Description: Formula-building inference rule for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)
Hypothesis
Ref Expression
csbeq2i.1 B = C
Assertion
Ref Expression
csbeq2i [A / x]B = [A / x]C

Proof of Theorem csbeq2i
StepHypRef Expression
1 csbeq2i.1 . . . 4 B = C
21a1i 10 . . 3 ( ⊤ → B = C)
32csbeq2dv 3161 . 2 ( ⊤ → [A / x]B = [A / x]C)
43trud 1323 1 [A / x]B = [A / x]C
 Colors of variables: wff setvar class Syntax hints:   ⊤ wtru 1316   = 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:  csbvarg  3163  csbnest1g  3188  csbsng  3785  csbunig  3899  csbxpg  4813  csbrng  4966  csbresg  4976  csbfv12g  5336
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