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Theorem nfcsb 3170
 Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
nfcsb.1 xA
nfcsb.2 xB
Assertion
Ref Expression
nfcsb x[A / y]B

Proof of Theorem nfcsb
StepHypRef Expression
1 nftru 1554 . . 3 y
2 nfcsb.1 . . . 4 xA
32a1i 10 . . 3 ( ⊤ → xA)
4 nfcsb.2 . . . 4 xB
54a1i 10 . . 3 ( ⊤ → xB)
61, 3, 5nfcsbd 3169 . 2 ( ⊤ → x[A / y]B)
76trud 1323 1 x[A / y]B
 Colors of variables: wff setvar class Syntax hints:   ⊤ wtru 1316  Ⅎwnfc 2476  [csb 3136 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  cbvralcsf  3198  cbvreucsf  3200  cbvrabcsf  3201  fmpt2x  5730
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