Theorem pm3.24 852

Description: Law of noncontradiction. Theorem *3.24 of [WhiteheadRussell] p. 111 (who call it the "law of contradiction"). (Contributed by NM, 16-Sep-1993.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)

Assertion

Ref	Expression
pm3.24	|- -. (ph /\ -. ph)

Proof of Theorem pm3.24

Step	Hyp	Ref	Expression
1		id 19	. 2 |- (ph -> ph)
2		iman 413	. 2 |- ((ph -> ph) <-> -. (ph /\ -. ph))
3	1, 2	mpbi 199	1 |- -. (ph /\ -. ph)

Syntax hints:  -. wn 3   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  pm4.43  893  nonconne  2523  pssirr  3369  indifdir  3511  dfnul2  3552  dfnul3  3553  rabnc  3574  nincompl  4072  imadif  5171