Theorem pm3.24 688

Description: Law of noncontradiction. Theorem *3.24 of [WhiteheadRussell] p. 111 (who call it the "law of contradiction"). (Contributed by NM, 16-Sep-1993.) (Revised by Mario Carneiro, 2-Feb-2015.)

Assertion

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

Proof of Theorem pm3.24

Step	Hyp	Ref	Expression
1		notnot 624	. 2 |- ( ph -> -. -. ph )
2		imnan 685	. 2 |- ( ( ph -> -. -. ph ) <-> -. ( ph /\ -. ph ) )
3	1, 2	mpbi 144	1 |- -. ( ph /\ -. ph )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  nnexmid  845  pm4.43  944  excxor  1373  nonconne  2352  dfnul2  3416  dfnul3  3417  rabnc  3447  axnul  4114  fiintim  6906  zeoxor  11828  unennn  12352