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Theorem nfiin 4122
 Description: Bound-variable hypothesis builder for indexed intersection. (Contributed by Mario Carneiro, 25-Jan-2014.)
Hypotheses
Ref Expression
nfiun.1
nfiun.2
Assertion
Ref Expression
nfiin

Proof of Theorem nfiin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iin 4098 . 2
2 nfiun.1 . . . 4
3 nfiun.2 . . . . 5
43nfcri 2568 . . . 4
52, 4nfral 2761 . . 3
65nfab 2578 . 2
71, 6nfcxfr 2571 1
 Colors of variables: wff set class Syntax hints:   wcel 1726  cab 2424  wnfc 2561  wral 2707  ciin 4096 This theorem is referenced by:  iinab  4154 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-iin 4098
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