Metamath Proof Explorer


Theorem 3bior1fd

Description: A disjunction is equivalent to a threefold disjunction with single falsehood, analogous to biorf . (Contributed by Alexander van der Vekens, 8-Sep-2017)

Ref Expression
Hypothesis 3biorfd.1 φ¬θ
Assertion 3bior1fd φχψθχψ

Proof

Step Hyp Ref Expression
1 3biorfd.1 φ¬θ
2 biorf ¬θχψθχψ
3 1 2 syl φχψθχψ
4 3orass θχψθχψ
5 3 4 bitr4di φχψθχψ