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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-jarli | Structured version Visualization version GIF version |
Description: Dropping a nested consequent. This theorem is one of two reversions of ja 173. Since ja 173 is reversible, one can conclude, that a nested (chain of) implication(s) is just a packed notation of two or more theorems/ hypotheses with a common consequent. axc5c7 34196 is an instance of this idea. (Contributed by Wolf Lammen, 4-Oct-2013.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
wl-jarli.1 | ⊢ ((𝜑 → 𝜓) → 𝜒) |
Ref | Expression |
---|---|
wl-jarli | ⊢ (¬ 𝜑 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.21 120 | . 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓)) | |
2 | wl-jarli.1 | . 2 ⊢ ((𝜑 → 𝜓) → 𝜒) | |
3 | 1, 2 | syl 17 | 1 ⊢ (¬ 𝜑 → 𝜒) |
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) |
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