Metamath Proof Explorer


Definition df-bnj17

Description: Define the 4-way conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Assertion df-bnj17
|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps /\ ch ) /\ th ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 wph
 |-  ph
1 wps
 |-  ps
2 wch
 |-  ch
3 wth
 |-  th
4 0 1 2 3 w-bnj17
 |-  ( ph /\ ps /\ ch /\ th )
5 0 1 2 w3a
 |-  ( ph /\ ps /\ ch )
6 5 3 wa
 |-  ( ( ph /\ ps /\ ch ) /\ th )
7 4 6 wb
 |-  ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps /\ ch ) /\ th ) )