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Theorem pm13.13a 27475
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 3131 . 2  |-  ( x  =  A  ->  ( ph 
<-> 
[. A  /  x ]. ph ) )
21biimpac 473 1  |-  ( (
ph  /\  x  =  A )  ->  [. A  /  x ]. ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    = wceq 1649   [.wsbc 3121
This theorem is referenced by:  pm13.194  27480
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-11 1757  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-sbc 3122
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