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Metamath Proof Explorer

Theorem biorfd

Description: A wff is equivalent to its disjunction with falsehood, deduction form. (Contributed by Peter Mazsa, 22-Aug-2023)

Ref Expression
Hypothesis biorfd.1 
|- ( ph -> -. ps )
Assertion biorfd 
|- ( ph -> ( ch <-> ( ps \/ ch ) ) )

Proof

Step Hyp Ref Expression
1 biorfd.1 
 |-  ( ph -> -. ps )
2 biorf 
 |-  ( -. ps -> ( ch <-> ( ps \/ ch ) ) )
3 1 2 syl 
 |-  ( ph -> ( ch <-> ( ps \/ ch ) ) )