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Theorem nfsbc1 3790
Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 5-Aug-1993.) (Revised 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 11 . . 3 (⊤ → 𝑥𝐴)
32nfsbc1d 3789 . 2 (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑)
43mptru 1535 1 𝑥[𝐴 / 𝑥]𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1529  wnf 1775  wnfc 2961  [wsbc 3771
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2793
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-sbc 3772
This theorem is referenced by:  nfsbc1v  3791  riotass2  7133  riotass  7134  uzwo4  41195
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