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Theorem pm13.13a 27710
Description: One result of theorem *13.13 in [WhiteheadRussell] p. 178. A note on the section - to make the theorems more usable, and because inequality is notation for set theory (it is not defined in the predicate calculus section), this section will use classes instead of sets. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.13a  |-  ( (
ph  /\  x  =  A )  ->  [. A  /  x ]. ph )

Proof of Theorem pm13.13a
StepHypRef Expression
1 sbceq1a 3014 . 2  |-  ( x  =  A  ->  ( ph 
<-> 
[. A  /  x ]. ph ) )
21biimpac 472 1  |-  ( (
ph  /\  x  =  A )  ->  [. A  /  x ]. ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    = wceq 1632   [.wsbc 3004
This theorem is referenced by:  pm13.194  27715
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-sbc 3005
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