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Mirrors > Home > ILE Home > Th. List > con3dimp | GIF version |
Description: Variant of con3d 621 with importation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
con3dimp.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
con3dimp | ⊢ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con3dimp.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | con3d 621 | . 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓)) |
3 | 2 | imp 123 | 1 ⊢ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-in1 604 ax-in2 605 |
This theorem is referenced by: nelneq 2265 nelneq2 2266 nelss 3201 nnnninf 7084 bcpasc 10673 fiinfnf1o 10693 nnoddn2prmb 12188 pcprod 12270 pw1nct 13776 |
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