3or6 - Metamath Proof Explorer

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Theorem 3or6 1410

Description: Analogue of or4 550 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011.)

**Assertion**
Ref	Expression
3or6	$\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$

**Proof of Theorem 3or6**
Step	Hyp	Ref	Expression
1		or4 550	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
2		or4 550	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
3	2	orbi1i 542	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
4	1, 3	bitr2i 265	. 2 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
5		df-3or 1038	. 2 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
6		df-3or 1038	. . 3 $\/$ $\/$ $\/$ $\/$
7		df-3or 1038	. . 3 $\/$ $\/$ $\/$ $\/$
8	6, 7	orbi12i 543	. 2 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
9	4, 5, 8	3bitr4i 292	1 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wb 196 $\/$ wo 383 $\/$ w3o 1036

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8

This theorem depends on definitions: df-bi 197 df-or 385 df-3or 1038

This theorem is referenced by: (None)