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Theorem notnot1 543
Description: Adding double negation. Theorem *2.12 of [WhiteheadRussell] p. 101. This one holds intuitionistically, but its converse does not (see notnot2dc 728). (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 2-Mar-2013.)
Assertion
Ref Expression
notnot1 (φ → ¬ ¬ φ)

Proof of Theorem notnot1
StepHypRef Expression
1 id 17 . 2 φ → ¬ φ)
21con2i 541 1 (φ → ¬ ¬ φ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem is referenced by:  con3d  544  notnoti  556  pm3.24  609  notnotnot  610  biortn  645  dcn  724  con1dc  729  notnotdc  742  eueq2dc  2595
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 528  ax-in2 529
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