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Theorem nabi12i 24904
Description: Constructor rule for  -/\. (Contributed by Anthony Hart, 2-Sep-2011.)
Hypotheses
Ref Expression
nabi12i.1  |-  ( ph  <->  ps )
nabi12i.2  |-  ( ch  <->  th )
nabi12i.3  |-  ( ps 
-/\  th )
Assertion
Ref Expression
nabi12i  |-  ( ph  -/\ 
ch )

Proof of Theorem nabi12i
StepHypRef Expression
1 nabi12i.2 . 2  |-  ( ch  <->  th )
2 nabi12i.1 . . 3  |-  ( ph  <->  ps )
3 nabi12i.3 . . 3  |-  ( ps 
-/\  th )
42, 3nabi1i 24902 . 2  |-  ( ph  -/\ 
th )
51, 4nabi2i 24903 1  |-  ( ph  -/\ 
ch )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    -/\ wnan 1287
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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