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Theorem notnot1 547
Description: Adding double negation. Theorem *2.12 of [WhiteheadRussell] p. 101. This one holds intuitionistically, but its converse does not (see notnot2dc 742). (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 19 . 2 φ → ¬ φ)
21con2i 545 1 (φ → ¬ ¬ φ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 532  ax-in2 533
This theorem is referenced by:  con3d  548  notnoti  561  pm3.24  614  notnotnot  615  biortn  651  dcn  737  dcimptest  744  con1dc  746  notnotdc  759  eueq2dc  2690  difsnpssim  3480  bdnthALT  6411
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