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Theorem pm13.13b 26775
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 2931 . 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 1619   [.wsbc 2921
This theorem is referenced by:  pm14.24  26799
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-12o 1664  ax-9 1684  ax-4 1692  ax-ext 2234
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-sbc 2922
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