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Theorem nfiin 3996
 Description: Bound-variable hypothesis builder for indexed intersection. (Contributed by Mario Carneiro, 25-Jan-2014.)
Hypotheses
Ref Expression
nfiun.1 yA
nfiun.2 yB
Assertion
Ref Expression
nfiin yx A B

Proof of Theorem nfiin
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 df-iin 3972 . 2 x A B = {z x A z B}
2 nfiun.1 . . . 4 yA
3 nfiun.2 . . . . 5 yB
43nfcri 2483 . . . 4 y z B
52, 4nfral 2667 . . 3 yx A z B
65nfab 2493 . 2 y{z x A z B}
71, 6nfcxfr 2486 1 yx A B
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1710  {cab 2339  Ⅎwnfc 2476  ∀wral 2614  ∩ciin 3970 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-or 359  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  df-ral 2619  df-iin 3972 This theorem is referenced by:  iinab  4027
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