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Theorem jcnd 163
Description: Deduction joining the consequents of two premises. (Contributed by Glauco Siliprandi, 11-Dec-2019.) (Proof shortened by Wolf Lammen, 10-Apr-2024.)
Hypotheses
Ref Expression
jcnd.1 (𝜑𝜓)
jcnd.2 (𝜑 → ¬ 𝜒)
Assertion
Ref Expression
jcnd (𝜑 → ¬ (𝜓𝜒))

Proof of Theorem jcnd
StepHypRef Expression
1 jcnd.1 . 2 (𝜑𝜓)
2 jcnd.2 . 2 (𝜑 → ¬ 𝜒)
3 jcn 162 . 2 (𝜓 → (¬ 𝜒 → ¬ (𝜓𝜒)))
41, 2, 3sylc 65 1 (𝜑 → ¬ (𝜓𝜒))
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:  nf1const  7302  isf34lem4  10372  strlem6  31509  hstrlem6  31517  nn0prpw  35208  unblimceq0  35383  relexpmulg  42461  limcrecl  44345  et-sqrtnegnre  45589  ichnreuop  46140
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