Theorem pm5.53 792

Description: Theorem *5.53 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.53	|- ( ( ( ( ph \/ ps ) \/ ch ) -> th ) <-> ( ( ( ph -> th ) /\ ( ps -> th ) ) /\ ( ch -> th ) ) )

Proof of Theorem pm5.53

Step	Hyp	Ref	Expression
1		jaob 700	. 2 |- ( ( ( ( ph \/ ps ) \/ ch ) -> th ) <-> ( ( ( ph \/ ps ) -> th ) /\ ( ch -> th ) ) )
2		jaob 700	. . 3 |- ( ( ( ph \/ ps ) -> th ) <-> ( ( ph -> th ) /\ ( ps -> th ) ) )
3	2	anbi1i 454	. 2 |- ( ( ( ( ph \/ ps ) -> th ) /\ ( ch -> th ) ) <-> ( ( ( ph -> th ) /\ ( ps -> th ) ) /\ ( ch -> th ) ) )
4	1, 3	bitri 183	1 |- ( ( ( ( ph \/ ps ) \/ ch ) -> th ) <-> ( ( ( ph -> th ) /\ ( ps -> th ) ) /\ ( ch -> th ) ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104   \/ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)