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Theorem pm13.13a 27618
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 3003 . 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 1625   [.wsbc 2993
This theorem is referenced by:  pm13.194  27623
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-11 1717  ax-ext 2266
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1531  df-sb 1632  df-clab 2272  df-cleq 2278  df-clel 2281  df-sbc 2994
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