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Theorem nfsbc1 2972
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 2971 . 2 (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑)
43mptru 1357 1 𝑥[𝐴 / 𝑥]𝜑
Colors of variables: wff set class
Syntax hints:  wtru 1349  wnf 1453  wnfc 2299  [wsbc 2955
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-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-sbc 2956
This theorem is referenced by:  nfsbc1v  2973  riotass2  5835  riotass  5836  bj-intabssel  13824
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