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Theorem nfaba1 2903
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 14-Oct-2016.) Add disjoint variable condition to avoid ax-13 2363. See nfaba1g 2904 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 2140 . 2 𝑥𝑥𝜑
21nfab 2901 1 𝑥{𝑦 ∣ ∀𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wal 1531  {cab 2701  wnfc 2875
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 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-11 2146  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-or 845  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2702  df-nfc 2877
This theorem is referenced by:  nfopd  4883  nfimad  6059  nfiota1  6488  nffvd  6894  nfunidALT2  38343  nfunidALT  38344  nfopdALT  38345  setrec1  47984
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