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| Mirrors > Home > MPE Home > Th. List > con4i | Structured version Visualization version GIF version | ||
| Description: Inference associated with
con4 113. Its associated inference is mt4 116.
Remark: this can also be proved using notnot 142 followed by nsyl2 141, giving a shorter proof but depending on more axioms (namely, ax-1 6 and ax-2 7). (Contributed by NM, 29-Dec-1992.) |
| Ref | Expression |
|---|---|
| con4i.1 | ⊢ (¬ 𝜑 → ¬ 𝜓) |
| Ref | Expression |
|---|---|
| con4i | ⊢ (𝜓 → 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | con4i.1 | . 2 ⊢ (¬ 𝜑 → ¬ 𝜓) | |
| 2 | con4 113 | . 2 ⊢ ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → 𝜑)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜓 → 𝜑) |
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