Metamath Proof Explorer


Theorem cdleme43frv1snN

Description: Value of [_ R / s ]_ N when -. R .<_ ( P .\/ Q ) . (Contributed by NM, 30-Mar-2013) (New usage is discouraged.)

Ref Expression
Hypotheses cdlemefr27.b B = Base K
cdlemefr27.l ˙ = K
cdlemefr27.j ˙ = join K
cdlemefr27.m ˙ = meet K
cdlemefr27.a A = Atoms K
cdlemefr27.h H = LHyp K
cdlemefr27.u U = P ˙ Q ˙ W
cdlemefr27.c C = s ˙ U ˙ Q ˙ P ˙ s ˙ W
cdlemefr27.n N = if s ˙ P ˙ Q I C
cdleme43fr.x X = R ˙ U ˙ Q ˙ P ˙ R ˙ W
Assertion cdleme43frv1snN R A ¬ R ˙ P ˙ Q R / s N = X

Proof

Step Hyp Ref Expression
1 cdlemefr27.b B = Base K
2 cdlemefr27.l ˙ = K
3 cdlemefr27.j ˙ = join K
4 cdlemefr27.m ˙ = meet K
5 cdlemefr27.a A = Atoms K
6 cdlemefr27.h H = LHyp K
7 cdlemefr27.u U = P ˙ Q ˙ W
8 cdlemefr27.c C = s ˙ U ˙ Q ˙ P ˙ s ˙ W
9 cdlemefr27.n N = if s ˙ P ˙ Q I C
10 cdleme43fr.x X = R ˙ U ˙ Q ˙ P ˙ R ˙ W
11 8 9 10 cdleme31sn2 R A ¬ R ˙ P ˙ Q R / s N = X