Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE 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 170 | . 2 ⊢ (𝜑 → (𝜃 ↔ 𝜃)) | |
2 | 3anbi1d.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
3 | 1, 2 | 3anbi13d 1245 | 1 ⊢ (𝜑 → ((𝜃 ∧ 𝜏 ∧ 𝜓) ↔ (𝜃 ∧ 𝜏 ∧ 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 103 ∧ w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: ceqsex3v 2641 ceqsex4v 2642 ceqsex8v 2644 vtocl3gaf 2667 mob 2774 ordsoexmid 4305 fseq1m1p1 9112 divalglemnn 10318 divalglemeunn 10321 divalglemex 10322 divalglemeuneg 10323 |
Copyright terms: Public domain | W3C validator |