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Mirrors > Home > ILE Home > Th. List > con3and | GIF version |
Description: Variant of con3d 561 with importation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
con3and.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
con3and | ⊢ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con3and.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | con3d 561 | . 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓)) |
3 | 2 | imp 115 | 1 ⊢ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-in1 544 ax-in2 545 |
This theorem is referenced by: nelneq 2138 nelneq2 2139 |
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