Theorem pm5.61 693

Description: Theorem *5.61 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 30-Jun-2013.)

Assertion

Ref	Expression
pm5.61	|- (((ph \/ ps) /\ -. ps) <-> (ph /\ -. ps))

Proof of Theorem pm5.61

Step	Hyp	Ref	Expression
1		biorf 394	. . 3 |- (-. ps -> (ph <-> (ps \/ ph)))
2		orcom 376	. . 3 |- ((ps \/ ph) <-> (ph \/ ps))
3	1, 2	syl6rbb 253	. 2 |- (-. ps -> ((ph \/ ps) <-> ph))
4	3	pm5.32ri 619	1 |- (((ph \/ ps) /\ -. ps) <-> (ph /\ -. ps))

This proof depends on syntax axioms:  -. wn 3   <-> wb 176   \/ wo 357   /\ 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-or 359  df-an 360

This theorem is used by:  pm5.75  903  nnsucelrlem2  4426