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Mirrors > Home > ILE Home > Th. List > imbi12d | GIF version |
Description: Deduction joining two equivalences to form equivalence of implications. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
imbi12d.1 | ⊢ (φ → (ψ ↔ χ)) |
imbi12d.2 | ⊢ (φ → (θ ↔ τ)) |
Ref | Expression |
---|---|
imbi12d | ⊢ (φ → ((ψ → θ) ↔ (χ → τ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imbi12d.1 | . . 3 ⊢ (φ → (ψ ↔ χ)) | |
2 | 1 | imbi1d 220 | . 2 ⊢ (φ → ((ψ → θ) ↔ (χ → θ))) |
3 | imbi12d.2 | . . 3 ⊢ (φ → (θ ↔ τ)) | |
4 | 3 | imbi2d 219 | . 2 ⊢ (φ → ((χ → θ) ↔ (χ → τ))) |
5 | 2, 4 | bitrd 177 | 1 ⊢ (φ → ((ψ → θ) ↔ (χ → τ))) |
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