Theorem pm5.4 249

Description: Antecedent absorption implication. Theorem *5.4 of [WhiteheadRussell] p. 125. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
pm5.4	|- ( ( ph -> ( ph -> ps ) ) <-> ( ph -> ps ) )

Proof of Theorem pm5.4

Step	Hyp	Ref	Expression
1		pm2.43 53	. 2 |- ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) )
2		ax-1 6	. 2 |- ( ( ph -> ps ) -> ( ph -> ( ph -> ps ) ) )
3	1, 2	impbii 126	1 |- ( ( ph -> ( ph -> ps ) ) <-> ( ph -> ps ) )

This proof depends on syntax axioms:   -> wi 4   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  imbibi  252  sbequ8  1900  moabs  2136  isprm4  12897  limcdifap  15763