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Theorem pm5.63 890
Description: Theorem *5.63 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 25-Dec-2012.)
Assertion
Ref Expression
pm5.63 ((φ ψ) ↔ (φ φ ψ)))

Proof of Theorem pm5.63
StepHypRef Expression
1 exmid 404 . . 3 (φ ¬ φ)
2 ordi 834 . . 3 ((φ φ ψ)) ↔ ((φ ¬ φ) (φ ψ)))
31, 2mpbiran 884 . 2 ((φ φ ψ)) ↔ (φ ψ))
43bicomi 193 1 ((φ ψ) ↔ (φ φ ψ)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  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:  cad1  1398
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