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Theorem 3pm3.2i 1160
 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 270 . 2 (𝜑𝜓)
4 3pm3.2i.3 . 2 𝜒
5 df-3an 965 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
63, 4, 5mpbir2an 927 1 (𝜑𝜓𝜒)
 Colors of variables: wff set class Syntax hints:   ∧ wa 103   ∧ w3a 963 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107 This theorem depends on definitions:  df-bi 116  df-3an 965 This theorem is referenced by:  mpbir3an  1164  3jaoi  1282  ftp  5614  4bc2eq6  10572  halfleoddlt  11647  strleun  12107  strle1g  12108  2irrexpqap  13123  ex-dvds  13133  nconstwlpolem0  13451
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