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Mirrors > Home > ILE Home > Th. List > biorfi | GIF version |
Description: A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995.) |
Ref | Expression |
---|---|
biorfi.1 | ⊢ ¬ φ |
Ref | Expression |
---|---|
biorfi | ⊢ (ψ ↔ (ψ ∨ φ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biorfi.1 | . 2 ⊢ ¬ φ | |
2 | orc 632 | . . 3 ⊢ (ψ → (ψ ∨ φ)) | |
3 | orel2 644 | . . 3 ⊢ (¬ φ → ((ψ ∨ φ) → ψ)) | |
4 | 2, 3 | impbid2 131 | . 2 ⊢ (¬ φ → (ψ ↔ (ψ ∨ φ))) |
5 | 1, 4 | ax-mp 7 | 1 ⊢ (ψ ↔ (ψ ∨ φ)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 98 ∨ wo 628 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in2 545 ax-io 629 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: pm4.43 855 dn1dc 866 excxor 1268 un0 3245 opthprc 4334 frec0g 5922 dcdc 9236 |
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