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Theorem im2anan9 810
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 453 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ch ) )
3 im2an9.2 . . 3  |-  ( th 
->  ( ta  ->  et ) )
43adantl 454 . 2  |-  ( (
ph  /\  th )  ->  ( ta  ->  et ) )
52, 4anim12d 548 1  |-  ( (
ph  /\  th )  ->  ( ( ps  /\  ta )  ->  ( ch 
/\  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360
This theorem is referenced by:  im2anan9r  811  ax11eq  2272  ax11el  2273  trin  4315  somo  4540  xpss12  4984  f1oun  5697  poxp  6461  soxp  6462  brecop  7000  ingru  8695  genpss  8886  genpnnp  8887  tgcl  17039  txlm  17685
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 179  df-an 362
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