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Mirrors > Home > ILE Home > Th. List > biorf | GIF version |
Description: A wff is equivalent to its disjunction with falsehood. Theorem *4.74 of [WhiteheadRussell] p. 121. (Contributed by NM, 23-Mar-1995.) (Proof shortened by Wolf Lammen, 18-Nov-2012.) |
Ref | Expression |
---|---|
biorf | ⊢ (¬ φ → (ψ ↔ (φ ∨ ψ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olc 631 | . 2 ⊢ (ψ → (φ ∨ ψ)) | |
2 | orel1 643 | . 2 ⊢ (¬ φ → ((φ ∨ ψ) → ψ)) | |
3 | 1, 2 | impbid2 131 | 1 ⊢ (¬ φ → (ψ ↔ (φ ∨ ψ))) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ↔ 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: biortn 663 pm5.61 707 pm5.55dc 818 euor 1923 eueq3dc 2709 difprsnss 3493 opthprc 4334 frecsuclem3 5929 swoord1 6071 indpi 6326 enq0tr 6417 mulap0r 7399 mulge0 7403 |
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