Theorem pm3.24 659

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 591	. 2 |- ( ph -> -. -. ph )
2		imnan 656	. 2 |- ( ( ph -> -. -. ph ) <-> -. ( ph /\ -. ph ) )
3	1, 2	mpbi 143	1 |- -. ( ph /\ -. ph )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm4.43  890  excxor  1309  nonconne  2257  dfnul2  3253  dfnul3  3254  rabnc  3277  axnul  3903  zeoxor  10268  nnexmid  10570