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Theorem nfsbc1 2841
 Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfsbc1.1 𝑥𝐴
Assertion
Ref Expression
nfsbc1 𝑥[𝐴 / 𝑥]𝜑

Proof of Theorem nfsbc1
StepHypRef Expression
1 nfsbc1.1 . . . 4 𝑥𝐴
21a1i 9 . . 3 (⊤ → 𝑥𝐴)
32nfsbc1d 2840 . 2 (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑)
43trud 1294 1 𝑥[𝐴 / 𝑥]𝜑
 Colors of variables: wff set class Syntax hints:  ⊤wtru 1286  Ⅎwnf 1390  Ⅎwnfc 2210  [wsbc 2824 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-sbc 2825 This theorem is referenced by:  nfsbc1v  2842  riotass2  5546  riotass  5547  bj-intabssel  10877
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