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Theorem 3orbi123 39215
 Description: pm4.39 951 with a 3-conjunct antecedent. This proof is 3orbi123VD 39580 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 1131 . 2 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) → (𝜑𝜓))
2 simp2 1132 . 2 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) → (𝜒𝜃))
3 simp3 1133 . 2 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) → (𝜏𝜂))
41, 2, 33orbi123d 1543 1 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) → ((𝜑𝜒𝜏) ↔ (𝜓𝜃𝜂)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196   ∨ w3o 1071   ∧ w3a 1072 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 197  df-or 384  df-an 385  df-3or 1073  df-3an 1074 This theorem is referenced by:  sbcoreleleq  39243  sbcoreleleqVD  39590
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