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Theorem pm13.13b 27007
Description: Theorem *13.13 in [WhiteheadRussell] p. 178 with different variable substitution. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.13b  |-  ( (
[. A  /  x ]. ph  /\  x  =  A )  ->  ph )

Proof of Theorem pm13.13b
StepHypRef Expression
1 sbceq1a 3002 . 2  |-  ( x  =  A  ->  ( ph 
<-> 
[. A  /  x ]. ph ) )
21biimparc 475 1  |-  ( (
[. A  /  x ]. ph  /\  x  =  A )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 6    /\ wa 360    = wceq 1628   [.wsbc 2992
This theorem is referenced by:  pm14.24  27031
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549  ax-17 1608  ax-9 1641  ax-8 1648  ax-11 1719  ax-ext 2265
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1534  df-sb 1636  df-clab 2271  df-cleq 2277  df-clel 2280  df-sbc 2993
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