Theorem biijust 636

Description: Theorem used to justify definition of intuitionistic biconditional df-bi 116. (Contributed by NM, 24-Nov-2017.)

Assertion

Ref	Expression
biijust	|- ( ( ( ( ph -> ps ) /\ ( ps -> ph ) ) -> ( ( ph -> ps ) /\ ( ps -> ph ) ) ) /\ ( ( ( ph -> ps ) /\ ( ps -> ph ) ) -> ( ( ph -> ps ) /\ ( ps -> ph ) ) ) )

Proof of Theorem biijust

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ( ph -> ps ) /\ ( ps -> ph ) ) -> ( ( ph -> ps ) /\ ( ps -> ph ) ) )
2	1, 1	pm3.2i 270	1 |- ( ( ( ( ph -> ps ) /\ ( ps -> ph ) ) -> ( ( ph -> ps ) /\ ( ps -> ph ) ) ) /\ ( ( ( ph -> ps ) /\ ( ps -> ph ) ) -> ( ( ph -> ps ) /\ ( ps -> ph ) ) ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107

This theorem is referenced by: (None)