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Mirrors > Home > NFE Home > Th. List > 3anbi3d | GIF version |
Description: Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.) |
Ref | Expression |
---|---|
3anbi1d.1 | ⊢ (φ → (ψ ↔ χ)) |
Ref | Expression |
---|---|
3anbi3d | ⊢ (φ → ((θ ∧ τ ∧ ψ) ↔ (θ ∧ τ ∧ χ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biidd 228 | . 2 ⊢ (φ → (θ ↔ θ)) | |
2 | 3anbi1d.1 | . 2 ⊢ (φ → (ψ ↔ χ)) | |
3 | 1, 2 | 3anbi13d 1254 | 1 ⊢ (φ → ((θ ∧ τ ∧ ψ) ↔ (θ ∧ τ ∧ χ))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∧ w3a 934 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936 |
This theorem is referenced by: ceqsex3v 2897 ceqsex4v 2898 ceqsex8v 2900 vtocl3gaf 2923 mob 3018 ins2keq 4218 ins3keq 4219 sikeq 4241 ceex 6174 elce 6175 |
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