Theorem pm4.81 355

Description: Theorem *4.81 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.81	|- ((-. ph -> ph) <-> ph)

Proof of Theorem pm4.81

Step	Hyp	Ref	Expression
1		pm2.18 102	. 2 |- ((-. ph -> ph) -> ph)
2		pm2.24 101	. 2 |- (ph -> (-. ph -> ph))
3	1, 2	impbii 180	1 |- ((-. ph -> ph) <-> ph)

This proof depends on syntax axioms:  -. wn 3   -> wi 4   <-> wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by: (None)