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Theorem nfabd 2787
 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{𝑦𝜓})

Proof of Theorem nfabd
StepHypRef Expression
1 nfabd.1 . 2 𝑦𝜑
2 nfabd.2 . . 3 (𝜑 → Ⅎ𝑥𝜓)
32adantr 481 . 2 ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → Ⅎ𝑥𝜓)
41, 3nfabd2 2786 1 (𝜑𝑥{𝑦𝜓})
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1478  Ⅎwnf 1705  {cab 2612  Ⅎwnfc 2754 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-9 2001  ax-10 2021  ax-11 2036  ax-12 2049  ax-13 2250  ax-ext 2606 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1883  df-clab 2613  df-cleq 2619  df-clel 2622  df-nfc 2756 This theorem is referenced by:  nfsbcd  3443  nfcsb1d  3533  nfcsbd  3536  nfifd  4091  nfunid  4414  nfiotad  5816  nfintd  41686  nfiund  41687
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