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Theorem nfaba1 2991
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 14-Oct-2016.) Add disjoint variable condition to avoid ax-13 2385. See nfaba1g 2992 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 2148 . 2 𝑥𝑥𝜑
21nfab 2989 1 𝑥{𝑦 ∣ ∀𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wal 1528  {cab 2804  wnfc 2966
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-10 2138  ax-11 2153  ax-12 2169
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-nfc 2968
This theorem is referenced by:  nfopd  4819  nfimad  5937  nfiota1  6315  nffvd  6681  nfunidALT2  35991  nfunidALT  35992  nfopdALT  35993  setrec1  44696
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