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Theorem im2anan9 843
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
im2anan9  |-  ( (
ph  /\  th )  ->  ( ( ps  /\  ta )  ->  ( ch 
/\  et ) ) )

Proof of Theorem im2anan9
StepHypRef Expression
1 im2an9.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21adantr 466 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ch ) )
3 im2an9.2 . . 3  |-  ( th 
->  ( ta  ->  et ) )
43adantl 467 . 2  |-  ( (
ph  /\  th )  ->  ( ta  ->  et ) )
52, 4anim12d 565 1  |-  ( (
ph  /\  th )  ->  ( ( ps  /\  ta )  ->  ( ch 
/\  et ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-an 372
This theorem is referenced by:  im2anan9r  844  trin  4471  somo  4751  xpss12  4902  f1oun  5793  poxp  6863  soxp  6864  brecop  7411  ingru  9191  genpss  9380  genpnnp  9381  tgcl  19927  txlm  20605  icorempt2  31661  ax12eq  32424  ax12el  32425
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