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Mirrors > Home > MPE Home > Th. List > Mathboxes > con3ALT2 | Structured version Visualization version GIF version |
Description: Contraposition. Alternate proof of con3 156. This proof is con3ALTVD 42209 automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
con3ALT2 | ⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnotr 132 | . . 3 ⊢ (¬ ¬ 𝜑 → 𝜑) | |
2 | 1 | imim1i 63 | . 2 ⊢ ((𝜑 → 𝜓) → (¬ ¬ 𝜑 → 𝜓)) |
3 | 2 | con1d 147 | 1 ⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → 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: (None) |
Copyright terms: Public domain | W3C validator |