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Theorem im2anan9r 809
Description: Deduction joining nested implications to form implication of conjunctions. (Contributed by NM, 29-Feb-1996.)
Hypotheses
Ref Expression
im2an9.1  |-  ( ph  ->  ( ps  ->  ch ) )
im2an9.2  |-  ( th 
->  ( ta  ->  et ) )
Assertion
Ref Expression
im2anan9r  |-  ( ( th  /\  ph )  ->  ( ( ps  /\  ta )  ->  ( ch 
/\  et ) ) )

Proof of Theorem im2anan9r
StepHypRef Expression
1 im2an9.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
2 im2an9.2 . . 3  |-  ( th 
->  ( ta  ->  et ) )
31, 2im2anan9 808 . 2  |-  ( (
ph  /\  th )  ->  ( ( ps  /\  ta )  ->  ( ch 
/\  et ) ) )
43ancoms 439 1  |-  ( ( th  /\  ph )  ->  ( ( ps  /\  ta )  ->  ( ch 
/\  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  pssnn  7081  lbreu  9704  catideu  13577  spwmo  14335  exidu1  20993  rngoideu  21051
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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