Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > cliftetb | Structured version Visualization version GIF version |
Description: show d is the same as an if-else involving a,b. (Contributed by Jarvin Udandy, 20-Sep-2020.) |
Ref | Expression |
---|---|
cliftetb.1 | ⊢ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒)) |
cliftetb.2 | ⊢ 𝜃 |
Ref | Expression |
---|---|
cliftetb | ⊢ (𝜃 ↔ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cliftetb.2 | . 2 ⊢ 𝜃 | |
2 | cliftetb.1 | . 2 ⊢ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒)) | |
3 | 1, 2 | 2th 267 | 1 ⊢ (𝜃 ↔ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 209 ∧ wa 399 ∨ wo 847 |
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 |
This theorem is referenced by: (None) |
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