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Mirrors > Home > MPE Home > Th. List > rb-ax2 | Structured version Visualization version GIF version |
Description: The second of four axioms in the Russell-Bernays axiom system. (Contributed by Anthony Hart, 13-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
rb-ax2 | ⊢ (¬ (𝜑 ∨ 𝜓) ∨ (𝜓 ∨ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm1.4 401 | . . . 4 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑)) | |
2 | 1 | con3i 150 | . . 3 ⊢ (¬ (𝜓 ∨ 𝜑) → ¬ (𝜑 ∨ 𝜓)) |
3 | 2 | con1i 144 | . 2 ⊢ (¬ ¬ (𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑)) |
4 | 3 | orri 391 | 1 ⊢ (¬ (𝜑 ∨ 𝜓) ∨ (𝜓 ∨ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∨ wo 383 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-or 385 |
This theorem is referenced by: rblem1 1682 rblem2 1683 rblem3 1684 rblem4 1685 rblem5 1686 rblem6 1687 re2luk1 1690 re2luk2 1691 re2luk3 1692 |
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