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Theorem xchnxbi 310
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)
Hypotheses
Ref Expression
xchnxbi.1  |-  ( -. 
ph 
<->  ps )
xchnxbi.2  |-  ( ph  <->  ch )
Assertion
Ref Expression
xchnxbi  |-  ( -. 
ch 
<->  ps )

Proof of Theorem xchnxbi
StepHypRef Expression
1 xchnxbi.2 . . 3  |-  ( ph  <->  ch )
21notbii 298 . 2  |-  ( -. 
ph 
<->  -.  ch )
3 xchnxbi.1 . 2  |-  ( -. 
ph 
<->  ps )
42, 3bitr3i 255 1  |-  ( -. 
ch 
<->  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 188
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 189
This theorem is referenced by:  xchnxbir  311  ioran  493  pm5.24  904  2mo  2379  necon1bbii  2672  nabbi  2724  psslinpr  9453  isprm2lem  14624
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