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Mirrors > Home > MPE Home > Th. List > ibd | Structured version Visualization version GIF version |
Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. Deduction associated with ibi 255. (Contributed by NM, 26-Jun-2004.) |
Ref | Expression |
---|---|
ibd.1 | ⊢ (𝜑 → (𝜓 → (𝜓 ↔ 𝜒))) |
Ref | Expression |
---|---|
ibd | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ibd.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜓 ↔ 𝜒))) | |
2 | biimp 204 | . 2 ⊢ ((𝜓 ↔ 𝜒) → (𝜓 → 𝜒)) | |
3 | 1, 2 | syli 38 | 1 ⊢ (𝜑 → (𝜓 → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 195 |
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 196 |
This theorem is referenced by: sssn 4298 unblem2 8098 atcv0eq 28622 atcv1 28623 atomli 28625 atcvatlem 28628 ibdr 33158 |
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