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Theorem 3simpc 903
Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
3simpc ((𝜑𝜓𝜒) → (𝜓𝜒))

Proof of Theorem 3simpc
StepHypRef Expression
1 3anrot 890 . 2 ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))
2 3simpa 901 . 2 ((𝜓𝜒𝜑) → (𝜓𝜒))
31, 2sylbi 114 1 ((𝜑𝜓𝜒) → (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  simp3  906  3adant1  922  3adantl1  1060  3adantr1  1063  eupickb  1981  find  4322  divcanap2  7657  diveqap0  7659  divrecap  7665  divcanap3  7673  eliooord  8795  fzrev3  8947  sqdivap  9316
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