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Theorem dvelimc 2302
Description: Version of dvelim 1992 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 1442 . . 3  |-  F/ x T.
2 nftru 1442 . . 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 2301 . 2  |-  ( T. 
->  ( -.  A. x  x  =  y  ->  F/_ x B ) )
109mptru 1340 1  |-  ( -. 
A. x  x  =  y  ->  F/_ x B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1329    = wceq 1331   T. wtru 1332   F/_wnfc 2268
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-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270
This theorem is referenced by:  nfcvf  2303
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