New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  nfabd GIF version

Theorem nfabd 2508
 Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
nfabd.1 yφ
nfabd.2 (φ → Ⅎxψ)
Assertion
Ref Expression
nfabd (φx{y ψ})

Proof of Theorem nfabd
StepHypRef Expression
1 nfabd.1 . 2 yφ
2 nfabd.2 . . 3 (φ → Ⅎxψ)
32adantr 451 . 2 ((φ ¬ x x = y) → Ⅎxψ)
41, 3nfabd2 2507 1 (φx{y ψ})
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540  Ⅎwnf 1544   = wceq 1642  {cab 2339  Ⅎwnfc 2476 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478 This theorem is referenced by:  nfsbcd  3066  nfcsb1d  3166  nfcsbd  3169  nfifd  3685  nfunid  3898  nfiotad  4342
 Copyright terms: Public domain W3C validator