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Mirrors > Home > MPE Home > Th. List > Mathboxes > al3im | Structured version Visualization version GIF version |
Description: Version of ax-4 1815 for a nested implication. (Contributed by RP, 13-Apr-2020.) |
Ref | Expression |
---|---|
al3im | ⊢ (∀𝑥(𝜑 → (𝜓 → (𝜒 → 𝜃))) → (∀𝑥𝜑 → (∀𝑥𝜓 → (∀𝑥𝜒 → ∀𝑥𝜃)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alim 1816 | . 2 ⊢ (∀𝑥(𝜑 → (𝜓 → (𝜒 → 𝜃))) → (∀𝑥𝜑 → ∀𝑥(𝜓 → (𝜒 → 𝜃)))) | |
2 | al2im 1820 | . 2 ⊢ (∀𝑥(𝜓 → (𝜒 → 𝜃)) → (∀𝑥𝜓 → (∀𝑥𝜒 → ∀𝑥𝜃))) | |
3 | 1, 2 | syl6 35 | 1 ⊢ (∀𝑥(𝜑 → (𝜓 → (𝜒 → 𝜃))) → (∀𝑥𝜑 → (∀𝑥𝜓 → (∀𝑥𝜒 → ∀𝑥𝜃)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1539 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-4 1815 |
This theorem is referenced by: (None) |
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