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Theorem im2anan9 831
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 465 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ch ) )
3 im2an9.2 . . 3  |-  ( th 
->  ( ta  ->  et ) )
43adantl 466 . 2  |-  ( (
ph  /\  th )  ->  ( ta  ->  et ) )
52, 4anim12d 563 1  |-  ( (
ph  /\  th )  ->  ( ( ps  /\  ta )  ->  ( ch 
/\  et ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
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 185  df-an 371
This theorem is referenced by:  im2anan9r  832  ax12eq  2251  ax12el  2252  trin  4506  somo  4786  xpss12  5056  f1oun  5771  poxp  6797  soxp  6798  brecop  7306  ingru  9097  genpss  9288  genpnnp  9289  tgcl  18716  txlm  19363
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