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Mirrors > Home > NFE Home > Th. List > ord | GIF version |
Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994.) |
Ref | Expression |
---|---|
ord.1 | ⊢ (φ → (ψ ∨ χ)) |
Ref | Expression |
---|---|
ord | ⊢ (φ → (¬ ψ → χ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ord.1 | . 2 ⊢ (φ → (ψ ∨ χ)) | |
2 | df-or 359 | . 2 ⊢ ((ψ ∨ χ) ↔ (¬ ψ → χ)) | |
3 | 1, 2 | sylib 188 | 1 ⊢ (φ → (¬ ψ → χ)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 357 |
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-or 359 |
This theorem is referenced by: orcanai 879 oplem1 930 ecase23d 1285 19.33b 1608 eqsn 3867 nnsucelr 4428 lenltfin 4469 vfin1cltv 4547 phi011lem1 4598 foconst 5280 nceleq 6149 addceq0 6219 ncslemuc 6255 nchoicelem8 6296 |
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