Metamath Proof Explorer


Definition df-propneg

Description: The negation of a sentence of propositional calculus is encoded by appending a one after the sentence. (Contributed by Thomas van Maaren, 21-Aug-2026)

Ref Expression
Assertion df-propneg
|- prop-. = ( x e. _V |-> ( x ++ <" 1 "> ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cpropneg
 |-  prop-.
1 vx
 |-  x
2 cvv
 |-  _V
3 1 cv
 |-  x
4 cconcat
 |-  ++
5 c1
 |-  1
6 5 cs1
 |-  <" 1 ">
7 3 6 4 co
 |-  ( x ++ <" 1 "> )
8 1 2 7 cmpt
 |-  ( x e. _V |-> ( x ++ <" 1 "> ) )
9 0 8 wceq
 |-  prop-. = ( x e. _V |-> ( x ++ <" 1 "> ) )