Theorem pclem6 896

Description: Negation inferred from embedded conjunct. (Contributed by NM, 20-Aug-1993.) (Proof shortened by Wolf Lammen, 25-Nov-2012.)

Assertion

Ref	Expression
pclem6	|- ((ph <-> (ps /\ -. ph)) -> -. ps)

Proof of Theorem pclem6

Step	Hyp	Ref	Expression
1		ibar 490	. . 3 |- (ps -> (-. ph <-> (ps /\ -. ph)))
2		nbbn 347	. . 3 |- ((-. ph <-> (ps /\ -. ph)) <-> -. (ph <-> (ps /\ -. ph)))
3	1, 2	sylib 188	. 2 |- (ps -> -. (ph <-> (ps /\ -. ph)))
4	3	con2i 112	1 |- ((ph <-> (ps /\ -. ph)) -> -. ps)

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)