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Theorem pm5.54 981
Description: Theorem *5.54 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 7-Nov-2013.)
Assertion
Ref Expression
pm5.54 (((𝜑𝜓) ↔ 𝜑) ∨ ((𝜑𝜓) ↔ 𝜓))

Proof of Theorem pm5.54
StepHypRef Expression
1 iba 525 . . . . 5 (𝜓 → (𝜑 ↔ (𝜑𝜓)))
21bicomd 213 . . . 4 (𝜓 → ((𝜑𝜓) ↔ 𝜑))
32adantl 473 . . 3 ((𝜑𝜓) → ((𝜑𝜓) ↔ 𝜑))
43, 2pm5.21ni 366 . 2 (¬ ((𝜑𝜓) ↔ 𝜑) → ((𝜑𝜓) ↔ 𝜓))
54orri 390 1 (((𝜑𝜓) ↔ 𝜑) ∨ ((𝜑𝜓) ↔ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wo 382  wa 383
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
This theorem is referenced by: (None)
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