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Theorem nfsbc1 3770
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 3769 . 2 (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑)
43mptru 1544 1 𝑥[𝐴 / 𝑥]𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1538  wnf 1784  wnfc 2957  [wsbc 3751
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2792
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2799  df-cleq 2813  df-clel 2891  df-nfc 2959  df-sbc 3752
This theorem is referenced by:  nfsbc1v  3771  riotass2  7119  riotass  7120  uzwo4  41457
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