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Theorem 3pm3.2i 1175
Description: Infer conjunction of premises. (Contributed by NM, 10-Feb-1995.)
Hypotheses
Ref Expression
3pm3.2i.1  |-  ph
3pm3.2i.2  |-  ps
3pm3.2i.3  |-  ch
Assertion
Ref Expression
3pm3.2i  |-  ( ph  /\ 
ps  /\  ch )

Proof of Theorem 3pm3.2i
StepHypRef Expression
1 3pm3.2i.1 . . 3  |-  ph
2 3pm3.2i.2 . . 3  |-  ps
31, 2pm3.2i 272 . 2  |-  ( ph  /\ 
ps )
4 3pm3.2i.3 . 2  |-  ch
5 df-3an 980 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
63, 4, 5mpbir2an 942 1  |-  ( ph  /\ 
ps  /\  ch )
Colors of variables: wff set class
Syntax hints:    /\ wa 104    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  mpbir3an  1179  3jaoi  1303  ftp  5703  4bc2eq6  10756  halfleoddlt  11901  strleun  12565  strle1g  12567  slotstnscsi  12655  slotsdnscsi  12679  slotsdifunifndx  12688  2irrexpqap  14435  lgslem2  14441  lgsdir2lem2  14469  lgsdir2lem3  14470  ex-dvds  14521  nconstwlpolem0  14850
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