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Mirrors > Home > MPE Home > Th. List > Mathboxes > tb-ax3 | Structured version Visualization version GIF version |
Description: The third of three axioms
in the Tarski-Bernays axiom system.
This axiom, along with ax-mp 5, tb-ax1 34210, and tb-ax2 34211, can be used to derive any theorem or rule that uses only →. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
tb-ax3 | ⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | peirce 205 | 1 ⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: re1ax2lem 34214 re1ax2 34215 |
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