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Axiom ax-2 8
Description: Axiom Frege. Axiom A2 of [Margaris] p. 49. One of the 3 axioms of propositional calculus. It "distributes" an antecedent over two consequents. This axiom was part of Frege's original system and is known as Frege in the literature. It is also proved as Theorem *2.77 of [WhiteheadRussell] p. 108. The other direction of this axiom also turns out to be true, as demonstrated by pm5.41 355. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-2  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  ->  ps )  ->  ( ph  ->  ch ) ) )

Detailed syntax breakdown of Axiom ax-2
StepHypRef Expression
1 wph . . 3  wff  ph
2 wps . . . 4  wff  ps
3 wch . . . 4  wff  ch
42, 3wi 6 . . 3  wff  ( ps 
->  ch )
51, 4wi 6 . 2  wff  ( ph  ->  ( ps  ->  ch ) )
61, 2wi 6 . . 3  wff  ( ph  ->  ps )
71, 3wi 6 . . 3  wff  ( ph  ->  ch )
86, 7wi 6 . 2  wff  ( (
ph  ->  ps )  -> 
( ph  ->  ch )
)
95, 8wi 6 1  wff  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  ->  ps )  ->  ( ph  ->  ch ) ) )
Colors of variables: wff set class
This axiom is referenced by:  a2i  14  id1  22  a2d  25  dfbi1gb  187  imdi  354  sbi1  2004  ralim  2617  difin0ss  3523  stoweidlem61  27211
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