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Mirrors > Home > ILE Home > Th. List > exbiri | GIF version |
Description: Inference form of exbir 1365. (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 291 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜃) → 𝜒) |
3 | 2 | exp31 356 | 1 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 ↔ wb 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: biimp3ar 1277 eqrdav 2080 tfrlem9 5958 lbreu 8023 uzsubsubfz 9066 elfzodifsumelfzo 9210 |
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