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Theorem nfcsb1 2881
 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 𝑥𝐴 / 𝑥𝐵

Proof of Theorem nfcsb1
StepHypRef Expression
1 nfcsb1.1 . . . 4 𝑥𝐴
21a1i 9 . . 3 (⊤ → 𝑥𝐴)
32nfcsb1d 2880 . 2 (⊤ → 𝑥𝐴 / 𝑥𝐵)
43trud 1252 1 𝑥𝐴 / 𝑥𝐵
 Colors of variables: wff set class Syntax hints:  ⊤wtru 1244  Ⅎwnfc 2165  ⦋csb 2852 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-sbc 2765  df-csb 2853 This theorem is referenced by:  nfcsb1v  2882
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