New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > ibd | GIF version |
Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. (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 | bi1 178 | . 2 ⊢ ((ψ ↔ χ) → (ψ → χ)) | |
3 | 1, 2 | syli 33 | 1 ⊢ (φ → (ψ → χ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 |
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 |
This theorem is referenced by: sssn 3864 |
Copyright terms: Public domain | W3C validator |