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Mirrors > Home > ILE Home > Th. List > biijust | GIF version |
Description: Theorem used to justify definition of intuitionistic biconditional df-bi 117. (Contributed by NM, 24-Nov-2017.) |
Ref | Expression |
---|---|
biijust | ⊢ ((((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑))) ∧ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑))) | |
2 | 1, 1 | pm3.2i 272 | 1 ⊢ ((((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑))) ∧ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 108 |
This theorem is referenced by: (None) |
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