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Theorem con1i 121
Description: A contraposition inference. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.) (Proof shortened by Wolf Lammen, 19-Jun-2013.)
Hypothesis
Ref Expression
con1i.a φψ)
Assertion
Ref Expression
con1i ψφ)

Proof of Theorem con1i
StepHypRef Expression
1 id 19 . 2 ψ → ¬ ψ)
2 con1i.a . 2 φψ)
31, 2nsyl2 119 1 ψφ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  nsyl4  134  pm2.24i  136  impi  140  simplim  143  pm3.13  487  pm5.55  867  rb-ax2  1518  rb-ax3  1519  rb-ax4  1520  ax17e  1618  spimfw  1646  hba1w  1707  ax5o  1749  hbnt  1775  hba1OLD  1787  nfndOLD  1792  hbimdOLD  1816  naecoms  1948  hba1-o  2149  ax467  2169  naecoms-o  2178  necon3bi  2557  necon1ai  2558  nfunsn  5353
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