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Theorem 3orel2OLD 1484
Description: Obsolete version of 3orel2 1483 as of 8-Oct-2025. (Contributed by Scott Fenton, 26-Mar-2011.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
3orel2OLD 𝜓 → ((𝜑𝜓𝜒) → (𝜑𝜒)))

Proof of Theorem 3orel2OLD
StepHypRef Expression
1 3orrot 1091 . 2 ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))
2 3orel1 1090 . . 3 𝜓 → ((𝜓𝜒𝜑) → (𝜒𝜑)))
3 orcom 870 . . 3 ((𝜒𝜑) ↔ (𝜑𝜒))
42, 3imbitrdi 251 . 2 𝜓 → ((𝜓𝜒𝜑) → (𝜑𝜒)))
51, 4biimtrid 242 1 𝜓 → ((𝜑𝜓𝜒) → (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 847  w3o 1085
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 207  df-or 848  df-3or 1087
This theorem is referenced by: (None)
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