Theorem pm5.33 617

Description: Theorem *5.33 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.33	|- ( ( ph /\ ( ps -> ch ) ) <-> ( ph /\ ( ( ph /\ ps ) -> ch ) ) )

Proof of Theorem pm5.33

Step	Hyp	Ref	Expression
1		ibar 301	. . 3 |- ( ph -> ( ps <-> ( ph /\ ps ) ) )
2	1	imbi1d 231	. 2 |- ( ph -> ( ( ps -> ch ) <-> ( ( ph /\ ps ) -> ch ) ) )
3	2	pm5.32i 458	1 |- ( ( ph /\ ( ps -> ch ) ) <-> ( ph /\ ( ( ph /\ ps ) -> ch ) ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by: (None)