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Theorem mptxor 1356
Description: Modus ponendo tollens 2, one of the "indemonstrables" in Stoic logic. Note that this uses exclusive-or  \/_. See rule 2 on [Lopez-Astorga] p. 12 , rule 4 on [Sanford] p. 39 and rule A4 in [Hitchcock] p. 5 . (Contributed by David A. Wheeler, 2-Mar-2018.)
Hypotheses
Ref Expression
mptxor.min  |-  ph
mptxor.maj  |-  ( ph  \/_ 
ps )
Assertion
Ref Expression
mptxor  |-  -.  ps

Proof of Theorem mptxor
StepHypRef Expression
1 mptxor.min . 2  |-  ph
2 mptxor.maj . . . 4  |-  ( ph  \/_ 
ps )
3 df-xor 1308 . . . 4  |-  ( (
ph  \/_  ps )  <->  ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) ) )
42, 3mpbi 143 . . 3  |-  ( (
ph  \/  ps )  /\  -.  ( ph  /\  ps ) )
54simpri 111 . 2  |-  -.  ( ph  /\  ps )
61, 5mptnan 1355 1  |-  -.  ps
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 102    \/ wo 662    \/_ wxo 1307
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  df-xor 1308
This theorem is referenced by: (None)
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