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Mirrors > Home > ILE Home > Th. List > truanOLD | GIF version |
Description: Obsolete proof of truan 1260 as of 21-Jul-2019. (Contributed by FL, 20-Mar-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
truanOLD | ⊢ ((⊤ ∧ 𝜑) ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 103 | . 2 ⊢ ((⊤ ∧ 𝜑) → 𝜑) | |
2 | a1tru 1259 | . . 3 ⊢ (𝜑 → ⊤) | |
3 | 2 | ancri 307 | . 2 ⊢ (𝜑 → (⊤ ∧ 𝜑)) |
4 | 1, 3 | impbii 117 | 1 ⊢ ((⊤ ∧ 𝜑) ↔ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 97 ↔ wb 98 ⊤wtru 1244 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-tru 1246 |
This theorem is referenced by: (None) |
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