Theorem pm4.15 694

Description: Theorem *4.15 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 18-Nov-2012.)

Assertion

Ref	Expression
pm4.15	|- ( ( ( ph /\ ps ) -> -. ch ) <-> ( ( ps /\ ch ) -> -. ph ) )

Proof of Theorem pm4.15

Step	Hyp	Ref	Expression
1		con2b 669	. 2 |- ( ( ( ps /\ ch ) -> -. ph ) <-> ( ph -> -. ( ps /\ ch ) ) )
2		nan 692	. 2 |- ( ( ph -> -. ( ps /\ ch ) ) <-> ( ( ph /\ ps ) -> -. ch ) )
3	1, 2	bitr2i 185	1 |- ( ( ( ph /\ ps ) -> -. ch ) <-> ( ( ps /\ ch ) -> -. ph ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)