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Theorem pm3.24 682
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
StepHypRef Expression
1 notnot 618 . 2  |-  ( ph  ->  -.  -.  ph )
2 imnan 679 . 2  |-  ( (
ph  ->  -.  -.  ph )  <->  -.  ( ph  /\  -.  ph ) )
31, 2mpbi 144 1  |-  -.  ( ph  /\  -.  ph )
Colors of variables: wff set class
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 603  ax-in2 604
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  nnexmid  835  pm4.43  933  excxor  1356  nonconne  2318  dfnul2  3360  dfnul3  3361  rabnc  3390  axnul  4048  fiintim  6810  zeoxor  11551  unennn  11895
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