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Theorem vtoclALT 3087
Description: Alternate proof of vtocl 3086. Shorter but requires more axioms. (Contributed by NM, 30-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
vtocl.1  |-  A  e. 
_V
vtocl.2  |-  ( x  =  A  ->  ( ph 
<->  ps ) )
vtocl.3  |-  ph
Assertion
Ref Expression
vtoclALT  |-  ps
Distinct variable groups:    x, A    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem vtoclALT
StepHypRef Expression
1 nfv 1769 . 2  |-  F/ x ps
2 vtocl.1 . 2  |-  A  e. 
_V
3 vtocl.2 . 2  |-  ( x  =  A  ->  ( ph 
<->  ps ) )
4 vtocl.3 . 2  |-  ph
51, 2, 3, 4vtoclf 3085 1  |-  ps
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189    = wceq 1452    e. wcel 1904   _Vcvv 3031
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-ext 2451
This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-v 3033
This theorem is referenced by: (None)
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