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Mirrors > Home > ILE Home > Th. List > pm2.27 | GIF version |
Description: This theorem, called "Assertion," can be thought of as closed form of modus ponens ax-mp 5. Theorem *2.27 of [WhiteheadRussell] p. 104. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
pm2.27 | ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓)) | |
2 | 1 | com12 30 | 1 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: pm2.43 53 com23 78 biimt 240 pm3.35 345 pm3.2im 627 jcn 641 pm2.65 649 annimim 676 condcOLD 844 pm2.26dc 897 ax10o 1702 issref 4980 acexmidlem2 5833 findcard2 6846 findcard2s 6847 xpfi 6886 exmidontriim 7172 pcmptcl 12251 txlm 12826 bj-inf2vnlem1 13693 bj-findis 13702 |
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