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

Theorem nfiunya 3679
Description: Bound-variable hypothesis builder for indexed union. (Contributed by Mario Carneiro, 25-Jan-2014.)
Hypotheses
Ref Expression
nfiunya.1 yA
nfiunya.2 yB
Assertion
Ref Expression
nfiunya y x A B
Distinct variable group:   x,A
Allowed substitution hints:   A(y)   B(x,y)

Proof of Theorem nfiunya
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 df-iun 3653 . 2 x A B = {zx A z B}
2 nfiunya.1 . . . 4 yA
3 nfiunya.2 . . . . 5 yB
43nfcri 2172 . . . 4 y z B
52, 4nfrexya 2360 . . 3 yx A z B
65nfab 2182 . 2 y{zx A z B}
71, 6nfcxfr 2175 1 y x A B
Colors of variables: wff set class
Syntax hints:   wcel 1393  {cab 2026  wnfc 2165  wrex 2304   ciun 3651
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2309  df-iun 3653
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator