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Mirrors > Home > ILE Home > Th. List > exbiri | GIF version |
Description: Inference form of exbir 1325. (Contributed by Alan Sare, 31-Dec-2011.) (Proof shortened by Wolf Lammen, 27-Jan-2013.) |
Ref | Expression |
---|---|
exbiri.1 | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ↔ 𝜃)) |
Ref | Expression |
---|---|
exbiri | ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exbiri.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ↔ 𝜃)) | |
2 | 1 | biimpar 281 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜃) → 𝜒) |
3 | 2 | exp31 346 | 1 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ↔ wb 98 |
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 |
This theorem is referenced by: biimp3ar 1236 eqrdav 2039 tfrlem9 5935 uzsubsubfz 8911 elfzodifsumelfzo 9057 |
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