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Theorem pm13.13a 27584
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 3171 . 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 1652   [.wsbc 3161
This theorem is referenced by:  pm13.194  27589
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-sbc 3162
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