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Theorem pm2.18d 127
Description: Deduction form of the Clavius law pm2.18 128. (Contributed by FL, 12-Jul-2009.) (Proof shortened by Andrew Salmon, 7-May-2011.) Revised to shorten pm2.18 128. (Revised by Wolf Lammen, 17-Nov-2023.)
Hypothesis
Ref Expression
pm2.18d.1 (𝜑 → (¬ 𝜓𝜓))
Assertion
Ref Expression
pm2.18d (𝜑𝜓)

Proof of Theorem pm2.18d
StepHypRef Expression
1 id 22 . 2 (𝜑𝜑)
2 pm2.18d.1 . . 3 (𝜑 → (¬ 𝜓𝜓))
3 pm2.21 123 . . 3 𝜓 → (𝜓 → ¬ 𝜑))
42, 3sylcom 30 . 2 (𝜑 → (¬ 𝜓 → ¬ 𝜑))
51, 4mt4d 117 1 (𝜑𝜓)
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:  pm2.18  128  pm2.61d  179  pm2.18da  797  oplem1  1054  axc11n  2424  weniso  7281  infssuni  9208  ordtypelem10  9384  oismo  9397  rankval3b  9683  grur1  10677  sqeqd  14976  hausflimi  23237  minveclem4  24702  ovolunnul  24770  vitali  24883  itg2mono  25024  frgrncvvdeqlem8  28958  minvecolem4  29530  contrd  36360  fppr2odd  45534
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