New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > pm4.71rd | GIF version |
Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of [WhiteheadRussell] p. 120. (Contributed by NM, 10-Feb-2005.) |
Ref | Expression |
---|---|
pm4.71rd.1 | ⊢ (φ → (ψ → χ)) |
Ref | Expression |
---|---|
pm4.71rd | ⊢ (φ → (ψ ↔ (χ ∧ ψ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.71rd.1 | . 2 ⊢ (φ → (ψ → χ)) | |
2 | pm4.71r 612 | . 2 ⊢ ((ψ → χ) ↔ (ψ ↔ (χ ∧ ψ))) | |
3 | 1, 2 | sylib 188 | 1 ⊢ (φ → (ψ ↔ (χ ∧ ψ))) |
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: 2reu5 3044 ralss 3332 rexss 3333 nnsucelrlem2 4425 dfco2a 5081 feu 5242 funbrfv2b 5362 dffn5 5363 fnrnfv 5364 fniniseg 5371 eqfnfv2 5393 dff4 5421 dff13 5471 nmembers1lem3 6270 |
Copyright terms: Public domain | W3C validator |