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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-impchain-com-3.2.1 | Structured version Visualization version GIF version |
Description: This theorem is in fact a copy of com3r 87. The proof is an example of how to arrive at arbitrary permutations of antecedents, using only swapping theorems. The recursion principle is to first swap the correct antecedent to the position just before the consequent, and then employ a theorem handling an implication chain of length one less to reorder the others. (Contributed by Wolf Lammen, 17-Nov-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
wl-impchain-com-3.2.1.h1 | ⊢ (𝜃 → (𝜒 → (𝜓 → 𝜑))) |
Ref | Expression |
---|---|
wl-impchain-com-3.2.1 | ⊢ (𝜓 → (𝜃 → (𝜒 → 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-impchain-com-3.2.1.h1 | . . 3 ⊢ (𝜃 → (𝜒 → (𝜓 → 𝜑))) | |
2 | 1 | wl-impchain-com-2.3 35401 | . 2 ⊢ (𝜃 → (𝜓 → (𝜒 → 𝜑))) |
3 | 2 | wl-impchain-com-1.2 35397 | 1 ⊢ (𝜓 → (𝜃 → (𝜒 → 𝜑))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-luk1 35363 ax-luk2 35364 ax-luk3 35365 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |