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Theorem biijust 603
Description: Theorem used to justify definition of intuitionistic biconditional df-bi 115. (Contributed by NM, 24-Nov-2017.)
Assertion
Ref Expression
biijust ((((𝜑𝜓) ∧ (𝜓𝜑)) → ((𝜑𝜓) ∧ (𝜓𝜑))) ∧ (((𝜑𝜓) ∧ (𝜓𝜑)) → ((𝜑𝜓) ∧ (𝜓𝜑))))

Proof of Theorem biijust
StepHypRef Expression
1 id 19 . 2 (((𝜑𝜓) ∧ (𝜓𝜑)) → ((𝜑𝜓) ∧ (𝜓𝜑)))
21, 1pm3.2i 266 1 ((((𝜑𝜓) ∧ (𝜓𝜑)) → ((𝜑𝜓) ∧ (𝜓𝜑))) ∧ (((𝜑𝜓) ∧ (𝜓𝜑)) → ((𝜑𝜓) ∧ (𝜓𝜑))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106
This theorem is referenced by: (None)
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