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Theorem nfcsb1 3034
 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 3033 . 2 (⊤ → 𝑥𝐴 / 𝑥𝐵)
43mptru 1340 1 𝑥𝐴 / 𝑥𝐵
 Colors of variables: wff set class Syntax hints:  ⊤wtru 1332  Ⅎwnfc 2268  ⦋csb 3003 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-sbc 2910  df-csb 3004 This theorem is referenced by:  nfcsb1v  3035
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