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Mirrors > Home > MPE Home > Th. List > Mathboxes > 3impexpbicomiVD | Structured version Visualization version GIF version |
Description: Virtual deduction proof of 3impexpbicomi 41989. The following user's proof
is completed by invoking mmj2's unify command and using mmj2's
StepSelector to pick all remaining steps of the Metamath proof.
|
Ref | Expression |
---|---|
3impexpbicomiVD.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) |
Ref | Expression |
---|---|
3impexpbicomiVD | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3impexpbicomiVD.1 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) | |
2 | 3impexpbicom 41988 | . . 3 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) ↔ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃))))) | |
3 | 2 | biimpi 215 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) → (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃))))) |
4 | 1, 3 | e0a 42281 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∧ w3a 1085 |
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 206 df-an 396 df-3an 1087 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |