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Theorem pm13.13a 27018
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 3002 . 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 1623   [.wsbc 2992
This theorem is referenced by:  pm13.194  27023
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-11 1716  ax-ext 2265
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-sb 1631  df-clab 2271  df-cleq 2277  df-clel 2280  df-sbc 2993
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