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Mirrors > Home > MPE Home > Th. List > retbwax3 | Structured version Visualization version GIF version |
Description: tbw-ax3 1618 rederived from merco1 1629. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
retbwax3 | ⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | retbwax2 1632 | . 2 ⊢ (𝜑 → (𝜑 → 𝜑)) | |
2 | merco1lem7 1638 | . 2 ⊢ ((𝜑 → (𝜑 → 𝜑)) → (((𝜑 → 𝜓) → 𝜑) → 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 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 depends on definitions: df-bi 196 df-tru 1478 df-fal 1481 |
This theorem is referenced by: (None) |
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