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Theorem dvelimc 2249
Description: Version of dvelim 1941 for classes. (Contributed by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
dvelimc.1  |-  F/_ x A
dvelimc.2  |-  F/_ z B
dvelimc.3  |-  ( z  =  y  ->  A  =  B )
Assertion
Ref Expression
dvelimc  |-  ( -. 
A. x  x  =  y  ->  F/_ x B )

Proof of Theorem dvelimc
StepHypRef Expression
1 nftru 1400 . . 3  |-  F/ x T.
2 nftru 1400 . . 3  |-  F/ z T.
3 dvelimc.1 . . . 4  |-  F/_ x A
43a1i 9 . . 3  |-  ( T. 
->  F/_ x A )
5 dvelimc.2 . . . 4  |-  F/_ z B
65a1i 9 . . 3  |-  ( T. 
->  F/_ z B )
7 dvelimc.3 . . . 4  |-  ( z  =  y  ->  A  =  B )
87a1i 9 . . 3  |-  ( T. 
->  ( z  =  y  ->  A  =  B ) )
91, 2, 4, 6, 8dvelimdc 2248 . 2  |-  ( T. 
->  ( -.  A. x  x  =  y  ->  F/_ x B ) )
109mptru 1298 1  |-  ( -. 
A. x  x  =  y  ->  F/_ x B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1287    = wceq 1289   T. wtru 1290   F/_wnfc 2215
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295  df-nf 1395  df-sb 1693  df-cleq 2081  df-clel 2084  df-nfc 2217
This theorem is referenced by:  nfcvf  2250
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