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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee3bir | Structured version Visualization version GIF version |
Description: Right-biconditional form of e3 37985 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 22-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee3bir.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
ee3bir.2 | ⊢ (𝜏 ↔ 𝜃) |
Ref | Expression |
---|---|
ee3bir | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee3bir.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | ee3bir.2 | . . 3 ⊢ (𝜏 ↔ 𝜃) | |
3 | 2 | biimpri 217 | . 2 ⊢ (𝜃 → 𝜏) |
4 | 1, 3 | syl8 74 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 195 |
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 196 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |