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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee102 | Structured version Visualization version GIF version |
Description: e102 37915 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee102.1 | ⊢ (𝜑 → 𝜓) |
ee102.2 | ⊢ 𝜒 |
ee102.3 | ⊢ (𝜑 → (𝜃 → 𝜏)) |
ee102.4 | ⊢ (𝜓 → (𝜒 → (𝜏 → 𝜂))) |
Ref | Expression |
---|---|
ee102 | ⊢ (𝜑 → (𝜃 → 𝜂)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee102.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | a1d 25 | . 2 ⊢ (𝜑 → (𝜃 → 𝜓)) |
3 | ee102.2 | . . . 4 ⊢ 𝜒 | |
4 | 3 | a1i 11 | . . 3 ⊢ (𝜃 → 𝜒) |
5 | 4 | a1i 11 | . 2 ⊢ (𝜑 → (𝜃 → 𝜒)) |
6 | ee102.3 | . 2 ⊢ (𝜑 → (𝜃 → 𝜏)) | |
7 | ee102.4 | . 2 ⊢ (𝜓 → (𝜒 → (𝜏 → 𝜂))) | |
8 | 2, 5, 6, 7 | ee222 37729 | 1 ⊢ (𝜑 → (𝜃 → 𝜂)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
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 df-an 385 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |