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Mirrors > Home > MPE Home > Th. List > jcn | Structured version Visualization version GIF version |
Description: Theorem joining the consequents of two premises. Theorem 8 of [Margaris] p. 60. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) |
Ref | Expression |
---|---|
jcn | ⊢ (𝜑 → (¬ 𝜓 → ¬ (𝜑 → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.27 42 | . 2 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓)) | |
2 | 1 | con3d 152 | 1 ⊢ (𝜑 → (¬ 𝜓 → ¬ (𝜑 → 𝜓))) |
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: jcnd 163 jath 33658 nmotru 34583 meran1 34586 onpsstopbas 34605 bj-brrelex12ALT 35224 |
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