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Mirrors > Home > ILE Home > Th. List > 3impexpbicomi | GIF version |
Description: Deduction form of 3impexpbicom 1327. (Contributed by Alan Sare, 31-Dec-2011.) |
Ref | Expression |
---|---|
3impexpbicomi.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) |
Ref | Expression |
---|---|
3impexpbicomi | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3impexpbicomi.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) | |
2 | 1 | bicomd 129 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜏 ↔ 𝜃)) |
3 | 2 | 3exp 1103 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃)))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 98 ∧ w3a 885 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-3an 887 |
This theorem is referenced by: (None) |
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