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Theorem 4exmidOLD 997
Description: Obsolete proof of 4exmid 996 as of 29-Oct-2021. (Contributed by David Abernethy, 28-Jan-2014.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
4exmidOLD (((𝜑𝜓) ∨ (¬ 𝜑 ∧ ¬ 𝜓)) ∨ ((𝜑 ∧ ¬ 𝜓) ∨ (𝜓 ∧ ¬ 𝜑)))

Proof of Theorem 4exmidOLD
StepHypRef Expression
1 exmid 431 . 2 ((𝜑𝜓) ∨ ¬ (𝜑𝜓))
2 dfbi3 993 . . 3 ((𝜑𝜓) ↔ ((𝜑𝜓) ∨ (¬ 𝜑 ∧ ¬ 𝜓)))
3 xor 934 . . 3 (¬ (𝜑𝜓) ↔ ((𝜑 ∧ ¬ 𝜓) ∨ (𝜓 ∧ ¬ 𝜑)))
42, 3orbi12i 543 . 2 (((𝜑𝜓) ∨ ¬ (𝜑𝜓)) ↔ (((𝜑𝜓) ∨ (¬ 𝜑 ∧ ¬ 𝜓)) ∨ ((𝜑 ∧ ¬ 𝜓) ∨ (𝜓 ∧ ¬ 𝜑))))
51, 4mpbi 220 1 (((𝜑𝜓) ∨ (¬ 𝜑 ∧ ¬ 𝜓)) ∨ ((𝜑 ∧ ¬ 𝜓) ∨ (𝜓 ∧ ¬ 𝜑)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wo 383  wa 384
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 385  df-an 386
This theorem is referenced by: (None)
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