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Axiom ax-2 6
Description: Axiom Frege. Axiom A2 of [Margaris] p. 49. This axiom "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 pm5.41 244. (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 4 . . 3  wff  ( ps 
->  ch )
51, 4wi 4 . 2  wff  ( ph  ->  ( ps  ->  ch ) )
61, 2wi 4 . . 3  wff  ( ph  ->  ps )
71, 3wi 4 . . 3  wff  ( ph  ->  ch )
86, 7wi 4 . 2  wff  ( (
ph  ->  ps )  -> 
( ph  ->  ch )
)
95, 8wi 4 1  wff  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  ->  ps )  ->  ( ph  ->  ch ) ) )
Colors of variables: wff set class
This axiom is referenced by:  a2i  11  idALT  20  a2d  26  imdi  243  sbi1v  1787  ralim  2397
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