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Mirrors > Home > ILE Home > Th. List > pm2.53 | GIF version |
Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 789). (Contributed by NM, 3-Jan-2005.) (Revised by NM, 31-Jan-2015.) |
Ref | Expression |
---|---|
pm2.53 | ⊢ ((φ ∨ ψ) → (¬ φ → ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.24 551 | . 2 ⊢ (φ → (¬ φ → ψ)) | |
2 | ax-1 5 | . 2 ⊢ (ψ → (¬ φ → ψ)) | |
3 | 1, 2 | jaoi 635 | 1 ⊢ ((φ ∨ ψ) → (¬ φ → ψ)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∨ 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: ori 641 ord 642 orel1 643 pm2.63 712 notnot2dc 750 dfordc 790 pm5.6r 835 xorbin 1272 19.33b2 1517 onsucelsucexmid 4215 oprabidlem 5479 |
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