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Theorem nabi2i 24903
Description: Constructor rule for  -/\. (Contributed by Anthony Hart, 2-Sep-2011.)
Hypotheses
Ref Expression
nabi2i.1  |-  ( ph  <->  ps )
nabi2i.2  |-  ( ch 
-/\  ps )
Assertion
Ref Expression
nabi2i  |-  ( ch 
-/\  ph )

Proof of Theorem nabi2i
StepHypRef Expression
1 nabi2i.2 . 2  |-  ( ch 
-/\  ps )
2 nabi2i.1 . . . 4  |-  ( ph  <->  ps )
32bicomi 193 . . 3  |-  ( ps  <->  ph )
4 nabi2 24901 . . 3  |-  ( ( ps  <->  ph )  ->  (
( ch  -/\  ps )  <->  ( ch  -/\  ph ) ) )
53, 4ax-mp 8 . 2  |-  ( ( ch  -/\  ps )  <->  ( ch  -/\  ph ) )
61, 5mpbi 199 1  |-  ( ch 
-/\  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    -/\ wnan 1287
This theorem is referenced by:  nabi12i  24904
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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