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Mirrors > Home > ILE Home > Th. List > notnot1 | GIF version |
Description: Adding double negation. Theorem *2.12 of [WhiteheadRussell] p. 101. This one holds intuitionistically, but its converse does not (see notnot2dc 750). (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 2-Mar-2013.) |
Ref | Expression |
---|---|
notnot1 | ⊢ (φ → ¬ ¬ φ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (¬ φ → ¬ φ) | |
2 | 1 | con2i 557 | 1 ⊢ (φ → ¬ ¬ φ) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-in1 544 ax-in2 545 |
This theorem is referenced by: con3d 560 notnoti 573 pm3.24 626 notnotnot 627 biortn 663 dcn 745 con1dc 752 notnotdc 765 eueq2dc 2708 difsnpssim 3498 xrlttri3 8488 nltpnft 8500 ngtmnft 8501 bdnthALT 9290 |
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