Theorem pm4.15 564

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 324	. 2 |- (((ps /\ ch) -> -. ph) <-> (ph -> -. (ps /\ ch)))
2		nan 563	. 2 |- ((ph -> -. (ps /\ ch)) <-> ((ph /\ ps) -> -. ch))
3	1, 2	bitr2i 241	1 |- (((ph /\ ps) -> -. ch) <-> ((ps /\ ch) -> -. ph))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   <-> wb 176   /\ wa 358

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  df-an 360

This theorem is used by: (None)