3or6 - Intuitionistic Logic Explorer

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Theorem 3or6 1334

Description: Analog of or4 772 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011.)

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

**Proof of Theorem 3or6**
Step	Hyp	Ref	Expression
1		or4 772	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
2		or4 772	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
3	2	orbi1i 764	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
4	1, 3	bitr2i 185	. 2 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
5		df-3or 981	. 2 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
6		df-3or 981	. . 3 $\/$ $\/$ $\/$ $\/$
7		df-3or 981	. . 3 $\/$ $\/$ $\/$ $\/$
8	6, 7	orbi12i 765	. 2 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
9	4, 5, 8	3bitr4i 212	1 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$

Colors of variables: wff set class

Syntax hints:

wb 105 $\/$ wo 709 $\/$ w3o 979

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710

This theorem depends on definitions: df-bi 117 df-3or 981

This theorem is referenced by: (None)