4exmid - Metamath Proof Explorer

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Theorem 4exmid 997

Description: The disjunction of the four possible combinations of two wffs and their negations is always true. A four-way excluded middle (see exmid 431). (Contributed by David Abernethy, 28-Jan-2014.) (Proof shortened by NM, 29-Oct-2021.)

**Assertion**
Ref	Expression
4exmid	$/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$

**Proof of Theorem 4exmid**
Step	Hyp	Ref	Expression
1		pm5.24 996	. . 3 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
2	1	biimpi 206	. 2 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
3	2	orri 391	1 $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$

Colors of variables: wff setvar class

Syntax hints:

wn 3 $\/$ wo 383 $/\$ wa 384

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-an 386

This theorem is referenced by: clsk1indlem3 38341

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