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Mirrors > Home > NFE Home > Th. List > anbi2 | GIF version |
Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 16-Nov-2013.) |
Ref | Expression |
---|---|
anbi2 | ⊢ ((φ ↔ ψ) → ((χ ∧ φ) ↔ (χ ∧ ψ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ ((φ ↔ ψ) → (φ ↔ ψ)) | |
2 | 1 | anbi2d 684 | 1 ⊢ ((φ ↔ ψ) → ((χ ∧ φ) ↔ (χ ∧ ψ))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∧ wa 358 |
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 177 df-an 360 |
This theorem is referenced by: (None) |
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