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Theorem nabi1i 24830
Description: Constructor rule for  -/\. (Contributed by Anthony Hart, 2-Sep-2011.)
Hypotheses
Ref Expression
nabi1i.1  |-  ( ph  <->  ps )
nabi1i.2  |-  ( ps 
-/\  ch )
Assertion
Ref Expression
nabi1i  |-  ( ph  -/\ 
ch )

Proof of Theorem nabi1i
StepHypRef Expression
1 nabi1i.2 . 2  |-  ( ps 
-/\  ch )
2 nabi1i.1 . . . 4  |-  ( ph  <->  ps )
32bicomi 193 . . 3  |-  ( ps  <->  ph )
4 nabi1 24828 . . 3  |-  ( ( ps  <->  ph )  ->  (
( ps  -/\  ch )  <->  (
ph  -/\  ch ) ) )
53, 4ax-mp 8 . 2  |-  ( ( ps  -/\  ch )  <->  (
ph  -/\  ch ) )
61, 5mpbi 199 1  |-  ( ph  -/\ 
ch )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    -/\ wnan 1287
This theorem is referenced by:  nabi12i  24832
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-nan 1288
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