Theorem exp12bd

Description: The import-export theorem ( impexp ) for biconditionals (deduction form). (Contributed by Zhi Wang, 3-Sep-2024)

	Ref	Expression
Hypothesis	exp12bd.1	|- ( ph -> ( ( ( ps /\ ch ) -> th ) <-> ( ( ta /\ et ) -> ze ) ) )
Assertion	exp12bd	|- ( ph -> ( ( ps -> ( ch -> th ) ) <-> ( ta -> ( et -> ze ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		exp12bd.1	|- ( ph -> ( ( ( ps /\ ch ) -> th ) <-> ( ( ta /\ et ) -> ze ) ) )
2		impexp	|- ( ( ( ps /\ ch ) -> th ) <-> ( ps -> ( ch -> th ) ) )
3		impexp	|- ( ( ( ta /\ et ) -> ze ) <-> ( ta -> ( et -> ze ) ) )
4	1 2 3	3bitr3g	|- ( ph -> ( ( ps -> ( ch -> th ) ) <-> ( ta -> ( et -> ze ) ) ) )