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Theorem 3orbi123 41151
Description: pm4.39 974 with a 3-conjunct antecedent. This proof is 3orbi123VD 41490 automatically translated and minimized. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
3orbi123 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) → ((𝜑𝜒𝜏) ↔ (𝜓𝜃𝜂)))

Proof of Theorem 3orbi123
StepHypRef Expression
1 simp1 1133 . 2 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) → (𝜑𝜓))
2 simp2 1134 . 2 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) → (𝜒𝜃))
3 simp3 1135 . 2 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) → (𝜏𝜂))
41, 2, 33orbi123d 1432 1 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) → ((𝜑𝜒𝜏) ↔ (𝜓𝜃𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  w3o 1083  w3a 1084
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3or 1085  df-3an 1086
This theorem is referenced by:  sbcoreleleq  41175  sbcoreleleqVD  41499
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