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Mirrors > Home > MPE Home > Th. List > Mathboxes > uunTT1p1 | Structured version Visualization version GIF version |
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
uunTT1p1.1 | ⊢ ((⊤ ∧ 𝜑 ∧ ⊤) → 𝜓) |
Ref | Expression |
---|---|
uunTT1p1 | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3ancomb 1101 | . . . 4 ⊢ ((⊤ ∧ 𝜑 ∧ ⊤) ↔ (⊤ ∧ ⊤ ∧ 𝜑)) | |
2 | 3anass 1097 | . . . 4 ⊢ ((⊤ ∧ ⊤ ∧ 𝜑) ↔ (⊤ ∧ (⊤ ∧ 𝜑))) | |
3 | anabs5 663 | . . . 4 ⊢ ((⊤ ∧ (⊤ ∧ 𝜑)) ↔ (⊤ ∧ 𝜑)) | |
4 | 1, 2, 3 | 3bitri 300 | . . 3 ⊢ ((⊤ ∧ 𝜑 ∧ ⊤) ↔ (⊤ ∧ 𝜑)) |
5 | truan 1554 | . . 3 ⊢ ((⊤ ∧ 𝜑) ↔ 𝜑) | |
6 | 4, 5 | bitri 278 | . 2 ⊢ ((⊤ ∧ 𝜑 ∧ ⊤) ↔ 𝜑) |
7 | uunTT1p1.1 | . 2 ⊢ ((⊤ ∧ 𝜑 ∧ ⊤) → 𝜓) | |
8 | 6, 7 | sylbir 238 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∧ w3a 1089 ⊤wtru 1544 |
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 210 df-an 400 df-3an 1091 df-tru 1546 |
This theorem is referenced by: (None) |
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