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Mirrors > Home > ILE Home > Th. List > con3 | GIF version |
Description: Contraposition. Theorem *2.16 of [WhiteheadRussell] p. 103. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 13-Feb-2013.) |
Ref | Expression |
---|---|
con3 | ⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓)) | |
2 | 1 | con3d 621 | 1 ⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-in1 604 ax-in2 605 |
This theorem is referenced by: mtt 675 annimim 676 pm3.37 679 const 842 con34bdc 861 hbnt 1640 ralf0 3508 ltleletr 7972 ltnsym 7976 bj-nnsn 13468 bj-nnclavius 13472 |
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