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Theorem pm5.54 870
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 (((φ ψ) ↔ φ) ((φ ψ) ↔ ψ))

Proof of Theorem pm5.54
StepHypRef Expression
1 iba 489 . . . . 5 (ψ → (φ ↔ (φ ψ)))
21bicomd 192 . . . 4 (ψ → ((φ ψ) ↔ φ))
32adantl 452 . . 3 ((φ ψ) → ((φ ψ) ↔ φ))
43, 2pm5.21ni 341 . 2 (¬ ((φ ψ) ↔ φ) → ((φ ψ) ↔ ψ))
54orri 365 1 (((φ ψ) ↔ φ) ((φ ψ) ↔ ψ))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wo 357   wa 358
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 177  df-or 359  df-an 360
This theorem is referenced by: (None)
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