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Theorem 3jaoOLD 1543
Description: Obsolete version of 3jao 1542 as of 28-Jun-2022. (Contributed by NM, 8-Apr-1994.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
3jaoOLD (((𝜑𝜓) ∧ (𝜒𝜓) ∧ (𝜃𝜓)) → ((𝜑𝜒𝜃) → 𝜓))

Proof of Theorem 3jaoOLD
StepHypRef Expression
1 df-3or 1101 . 2 ((𝜑𝜒𝜃) ↔ ((𝜑𝜒) ∨ 𝜃))
2 jao 974 . . . 4 ((𝜑𝜓) → ((𝜒𝜓) → ((𝜑𝜒) → 𝜓)))
3 jao 974 . . . 4 (((𝜑𝜒) → 𝜓) → ((𝜃𝜓) → (((𝜑𝜒) ∨ 𝜃) → 𝜓)))
42, 3syl6 35 . . 3 ((𝜑𝜓) → ((𝜒𝜓) → ((𝜃𝜓) → (((𝜑𝜒) ∨ 𝜃) → 𝜓))))
543imp 1130 . 2 (((𝜑𝜓) ∧ (𝜒𝜓) ∧ (𝜃𝜓)) → (((𝜑𝜒) ∨ 𝜃) → 𝜓))
61, 5syl5bi 233 1 (((𝜑𝜓) ∧ (𝜒𝜓) ∧ (𝜃𝜓)) → ((𝜑𝜒𝜃) → 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 865  w3o 1099  w3a 1100
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 198  df-an 385  df-or 866  df-3or 1101  df-3an 1102
This theorem is referenced by: (None)
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