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Theorem pm13.13b 36661
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 3311 . 2  |-  ( x  =  A  ->  ( ph 
<-> 
[. A  /  x ]. ph ) )
21biimparc 490 1  |-  ( (
[. A  /  x ]. ph  /\  x  =  A )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 371    = wceq 1438   [.wsbc 3300
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-12 1906  ax-ext 2401
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1661  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-sbc 3301
This theorem is referenced by:  pm14.24  36685
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