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Axiom ax-3 8
 Description: Axiom Transp. Axiom A3 of [Margaris] p. 49. One of the 3 axioms of propositional calculus. It swaps or "transposes" the order of the consequents when negation is removed. An informal example is that the statement "if there are no clouds in the sky, it is not raining" implies the statement "if it is raining, there are clouds in the sky." This axiom is called Transp or "the principle of transposition" in Principia Mathematica (Theorem *2.17 of [WhiteheadRussell] p. 103). We will also use the term "contraposition" for this principle, although the reader is advised that in the field of philosophical logic, "contraposition" has a different technical meaning. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-3

Detailed syntax breakdown of Axiom ax-3
StepHypRef Expression
1 wph . . . 4
21wn 3 . . 3
3 wps . . . 4
43wn 3 . . 3
52, 4wi 4 . 2
63, 1wi 4 . 2
75, 6wi 4 1
 Colors of variables: wff set class This axiom is referenced by:  con4d  100  dfbi1gb  187  con34b  285  meredith  1414  ax3h  27851  notnot2ALTVD  29101  con3ALTVD  29102
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