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Theorem nfcsb1 3167
Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfcsb1.1 xA
Assertion
Ref Expression
nfcsb1 x[A / x]B

Proof of Theorem nfcsb1
StepHypRef Expression
1 nfcsb1.1 . . . 4 xA
21a1i 10 . . 3 ( ⊤ → xA)
32nfcsb1d 3166 . 2 ( ⊤ → x[A / x]B)
43trud 1323 1 x[A / x]B
Colors of variables: wff setvar class
Syntax hints:  wtru 1316  wnfc 2476  [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-nfc 2478  df-sbc 3047  df-csb 3137
This theorem is referenced by:  nfcsb1v  3168
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