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Mirrors > Home > NFE Home > Th. List > 3imtr3d | GIF version |
Description: More general version of 3imtr3i 256. Useful for converting conditional definitions in a formula. (Contributed by NM, 8-Apr-1996.) |
Ref | Expression |
---|---|
3imtr3d.1 | ⊢ (φ → (ψ → χ)) |
3imtr3d.2 | ⊢ (φ → (ψ ↔ θ)) |
3imtr3d.3 | ⊢ (φ → (χ ↔ τ)) |
Ref | Expression |
---|---|
3imtr3d | ⊢ (φ → (θ → τ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3imtr3d.2 | . 2 ⊢ (φ → (ψ ↔ θ)) | |
2 | 3imtr3d.1 | . . 3 ⊢ (φ → (ψ → χ)) | |
3 | 3imtr3d.3 | . . 3 ⊢ (φ → (χ ↔ τ)) | |
4 | 2, 3 | sylibd 205 | . 2 ⊢ (φ → (ψ → τ)) |
5 | 1, 4 | sylbird 226 | 1 ⊢ (φ → (θ → τ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 |
This theorem is referenced by: (None) |
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