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Theorem anandii 29107
Description: Elimination of dependent conjuncts. (Contributed by NM, 7-Nov-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
anandii.1  |-  ( ph  ->  ch )
anandii.2  |-  ( ps 
->  th )
Assertion
Ref Expression
anandii  |-  ( ( ( ch  /\  ps )  /\  ( ph  /\  th ) )  <->  ( ph  /\ 
ps ) )

Proof of Theorem anandii
StepHypRef Expression
1 an42 798 . 2  |-  ( ( ( ch  /\  ps )  /\  ( ph  /\  th ) )  <->  ( ( ch  /\  ph )  /\  ( th  /\  ps )
) )
2 anandii.1 . . . 4  |-  ( ph  ->  ch )
32pm4.71ri 614 . . 3  |-  ( ph  <->  ( ch  /\  ph )
)
4 anandii.2 . . . 4  |-  ( ps 
->  th )
54pm4.71ri 614 . . 3  |-  ( ps  <->  ( th  /\  ps )
)
63, 5anbi12i 678 . 2  |-  ( (
ph  /\  ps )  <->  ( ( ch  /\  ph )  /\  ( th  /\  ps ) ) )
71, 6bitr4i 243 1  |-  ( ( ( ch  /\  ps )  /\  ( ph  /\  th ) )  <->  ( ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  ax12conj2  29108  a12study8  29119
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
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