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	⊢ ((((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑))) ∧ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑))))

Proof of Theorem biijust

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)))
2	1, 1	pm3.2i 270	1 ⊢ ((((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑))) ∧ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑))))

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)