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Theorem nfdju 6895
Description: Bound-variable hypothesis builder for disjoint union. (Contributed by Jim Kingdon, 23-Jun-2022.)
Hypotheses
Ref Expression
nfdju.1  |-  F/_ x A
nfdju.2  |-  F/_ x B
Assertion
Ref Expression
nfdju  |-  F/_ x
( A B )

Proof of Theorem nfdju
StepHypRef Expression
1 df-dju 6891 . 2  |-  ( A B )  =  ( ( { (/) }  X.  A )  u.  ( { 1o }  X.  B
) )
2 nfcv 2258 . . . 4  |-  F/_ x { (/) }
3 nfdju.1 . . . 4  |-  F/_ x A
42, 3nfxp 4536 . . 3  |-  F/_ x
( { (/) }  X.  A )
5 nfcv 2258 . . . 4  |-  F/_ x { 1o }
6 nfdju.2 . . . 4  |-  F/_ x B
75, 6nfxp 4536 . . 3  |-  F/_ x
( { 1o }  X.  B )
84, 7nfun 3202 . 2  |-  F/_ x
( ( { (/) }  X.  A )  u.  ( { 1o }  X.  B ) )
91, 8nfcxfr 2255 1  |-  F/_ x
( A B )
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2245    u. cun 3039   (/)c0 3333   {csn 3497    X. cxp 4507   1oc1o 6274   ⊔ cdju 6890
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-un 3045  df-opab 3960  df-xp 4515  df-dju 6891
This theorem is referenced by: (None)
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