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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 𝜑
3pm3.2i.2 𝜓
3pm3.2i.3 𝜒
Assertion
Ref Expression
3pm3.2i (𝜑𝜓𝜒)

Proof of Theorem 3pm3.2i
StepHypRef Expression
1 3pm3.2i.1 . . 3 𝜑
2 3pm3.2i.2 . . 3 𝜓
31, 2pm3.2i 272 . 2 (𝜑𝜓)
4 3pm3.2i.3 . 2 𝜒
5 df-3an 980 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
63, 4, 5mpbir2an 942 1 (𝜑𝜓𝜒)
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  5701  4bc2eq6  10749  halfleoddlt  11893  strleun  12557  strle1g  12559  slotstnscsi  12644  slotsdnscsi  12668  slotsdifunifndx  12677  2irrexpqap  14327  lgslem2  14333  lgsdir2lem2  14361  lgsdir2lem3  14362  ex-dvds  14402  nconstwlpolem0  14730
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