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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-imim2ALT | Structured version Visualization version GIF version |
Description: More direct proof of imim2 56. Note that imim2i 16 and imim2d 55 can be proved as usual from this closed form (i.e., using ax-mp 5 and syl 17 respectively). (Contributed by BJ, 19-Jul-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bj-imim2ALT | ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜒 → (𝜑 → 𝜓))) | |
2 | 1 | a2d 29 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓))) |
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 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |