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Theorem pm3.24 660
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 592 . 2  |-  ( ph  ->  -.  -.  ph )
2 imnan 657 . 2  |-  ( (
ph  ->  -.  -.  ph )  <->  -.  ( ph  /\  -.  ph ) )
31, 2mpbi 143 1  |-  -.  ( ph  /\  -.  ph )
Colors of variables: wff set class
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 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm4.43  891  excxor  1310  nonconne  2258  dfnul2  3260  dfnul3  3261  rabnc  3284  axnul  3911  zeoxor  10413  unennn  10708  nnexmid  10721
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