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Theorem vtocld 2660
Description: Implicit substitution of a class for a setvar variable. (Contributed by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
vtocld.1  |-  ( ph  ->  A  e.  V )
vtocld.2  |-  ( (
ph  /\  x  =  A )  ->  ( ps 
<->  ch ) )
vtocld.3  |-  ( ph  ->  ps )
Assertion
Ref Expression
vtocld  |-  ( ph  ->  ch )
Distinct variable groups:    x, A    ph, x    ch, x
Allowed substitution hints:    ps( x)    V( x)

Proof of Theorem vtocld
StepHypRef Expression
1 vtocld.1 . 2  |-  ( ph  ->  A  e.  V )
2 vtocld.2 . 2  |-  ( (
ph  /\  x  =  A )  ->  ( ps 
<->  ch ) )
3 vtocld.3 . 2  |-  ( ph  ->  ps )
4 nfv 1462 . 2  |-  F/ x ph
5 nfcvd 2224 . 2  |-  ( ph  -> 
F/_ x A )
6 nfvd 1463 . 2  |-  ( ph  ->  F/ x ch )
71, 2, 3, 4, 5, 6vtocldf 2659 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103    = wceq 1285    e. wcel 1434
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-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-3an 922  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612
This theorem is referenced by:  funfvima3  5444  frec2uzuzd  9536
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