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Mirrors > Home > MPE Home > Th. List > Mathboxes > nabi2 | Structured version Visualization version GIF version |
Description: Constructor theorem for ⊼. (Contributed by Anthony Hart, 1-Sep-2011.) |
Ref | Expression |
---|---|
nabi2 | ⊢ ((𝜑 ↔ 𝜓) → ((𝜒 ⊼ 𝜑) ↔ (𝜒 ⊼ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nanbi2 1456 | 1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜒 ⊼ 𝜑) ↔ (𝜒 ⊼ 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 196 ⊼ wnan 1447 |
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 197 df-an 386 df-nan 1448 |
This theorem is referenced by: (None) |
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