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Mirrors > Home > NFE Home > Th. List > pm4.71d | GIF version |
Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of [WhiteheadRussell] p. 120. (Contributed by Mario Carneiro, 25-Dec-2016.) |
Ref | Expression |
---|---|
pm4.71rd.1 | ⊢ (φ → (ψ → χ)) |
Ref | Expression |
---|---|
pm4.71d | ⊢ (φ → (ψ ↔ (ψ ∧ χ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.71rd.1 | . 2 ⊢ (φ → (ψ → χ)) | |
2 | pm4.71 611 | . 2 ⊢ ((ψ → χ) ↔ (ψ ↔ (ψ ∧ χ))) | |
3 | 1, 2 | sylib 188 | 1 ⊢ (φ → (ψ ↔ (ψ ∧ χ))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∧ wa 358 |
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 |
This theorem is referenced by: ax12bOLD 1690 difin2 3516 |
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