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Theorem dvelimc 2453
Description: Version of dvelim 1969 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 1544 . . 3  |-  F/ x  T.
2 nftru 1544 . . 3  |-  F/ z  T.
3 dvelimc.1 . . . 4  |-  F/_ x A
43a1i 10 . . 3  |-  (  T. 
->  F/_ x A )
5 dvelimc.2 . . . 4  |-  F/_ z B
65a1i 10 . . 3  |-  (  T. 
->  F/_ z B )
7 dvelimc.3 . . . 4  |-  ( z  =  y  ->  A  =  B )
87a1i 10 . . 3  |-  (  T. 
->  ( z  =  y  ->  A  =  B ) )
91, 2, 4, 6, 8dvelimdc 2452 . 2  |-  (  T. 
->  ( -.  A. x  x  =  y  ->  F/_ x B ) )
109trud 1314 1  |-  ( -. 
A. x  x  =  y  ->  F/_ x B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    T. wtru 1307   A.wal 1530    = wceq 1632   F/_wnfc 2419
This theorem is referenced by:  nfcvf  2454
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-cleq 2289  df-clel 2292  df-nfc 2421
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