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Theorem 3pm3.2i 1093
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 261 . 2 (𝜑𝜓)
4 3pm3.2i.3 . 2 𝜒
5 df-3an 898 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
63, 4, 5mpbir2an 860 1 (𝜑𝜓𝜒)
Colors of variables: wff set class
Syntax hints:  wa 101  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  mpbir3an  1097  3jaoi  1209  ftp  5376  4bc2eq6  9642  halfleoddlt  10206  ex-dvds  10283
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