# Metamath Proof Explorer

## Theorem cdlemg16ALTN

Description: This version of cdlemg16 uses cdlemg15a instead of cdlemg15 , in case cdlemg15 ends up not being needed. TODO: FIX COMMENT. (Contributed by NM, 6-May-2013) (New usage is discouraged.)

Ref Expression
Hypotheses cdlemg12.l
cdlemg12.j
cdlemg12.m
cdlemg12.a ${⊢}{A}=\mathrm{Atoms}\left({K}\right)$
cdlemg12.h ${⊢}{H}=\mathrm{LHyp}\left({K}\right)$
cdlemg12.t ${⊢}{T}=\mathrm{LTrn}\left({K}\right)\left({W}\right)$
cdlemg12b.r ${⊢}{R}=\mathrm{trL}\left({K}\right)\left({W}\right)$
Assertion cdlemg16ALTN

### Proof

Step Hyp Ref Expression
1 cdlemg12.l
2 cdlemg12.j
3 cdlemg12.m
4 cdlemg12.a ${⊢}{A}=\mathrm{Atoms}\left({K}\right)$
5 cdlemg12.h ${⊢}{H}=\mathrm{LHyp}\left({K}\right)$
6 cdlemg12.t ${⊢}{T}=\mathrm{LTrn}\left({K}\right)\left({W}\right)$
7 cdlemg12b.r ${⊢}{R}=\mathrm{trL}\left({K}\right)\left({W}\right)$
8 simpl11
9 simpl12
10 8 9 jca
11 simpl21
12 simpl22
13 simpl13
14 simpr
15 simpl31
16 1 2 3 4 5 6 7 cdlemg15a
17 10 11 12 13 14 15 16 syl312anc
18 simpl11
19 simpl12
20 18 19 jca
21 simpl21
22 simpl22
23 simp13l