ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfaba1 GIF version

Theorem nfaba1 2288
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 14-Oct-2016.)
Assertion
Ref Expression
nfaba1 𝑥{𝑦 ∣ ∀𝑥𝜑}

Proof of Theorem nfaba1
StepHypRef Expression
1 nfa1 1522 . 2 𝑥𝑥𝜑
21nfab 2287 1 𝑥{𝑦 ∣ ∀𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  wal 1330  {cab 2126  wnfc 2269
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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-nfc 2271
This theorem is referenced by:  nfopd  3726  nfimad  4894  nfiota1  5094  nffvd  5437
  Copyright terms: Public domain W3C validator