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Mirrors > Home > MPE Home > Th. List > stdpc5v | Structured version Visualization version GIF version |
Description: Version of stdpc5 2203 with a disjoint variable condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020.) Revised to shorten 19.21v 1936. (Revised by Wolf Lammen, 12-Jul-2020.) |
Ref | Expression |
---|---|
stdpc5v | ⊢ (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-5 1907 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | alim 1807 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓)) | |
3 | 1, 2 | syl5 34 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1531 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-4 1806 ax-5 1907 |
This theorem is referenced by: 19.21v 1936 wl-moteq 34748 axc11next 40731 |
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