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Theorem nfaba1 2916
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 14-Oct-2016.) Add disjoint variable condition to avoid ax-13 2371. See nfaba1g 2917 for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 20-Jan-2024.)
Assertion
Ref Expression
nfaba1 𝑥{𝑦 ∣ ∀𝑥𝜑}
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfaba1
StepHypRef Expression
1 nfa1 2149 . 2 𝑥𝑥𝜑
21nfab 2914 1 𝑥{𝑦 ∣ ∀𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wal 1540  {cab 2714  wnfc 2888
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-10 2138  ax-11 2155  ax-12 2172
This theorem depends on definitions:  df-bi 206  df-or 847  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2715  df-nfc 2890
This theorem is referenced by:  nfopd  4852  nfimad  6027  nfiota1  6455  nffvd  6859  nfunidALT2  37460  nfunidALT  37461  nfopdALT  37462  setrec1  47210
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