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Theorem stdpc5v 2034
Description: Version of stdpc5 2242 with a disjoint variable condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020.) Revised to shorten 19.21v 2035. (Revised by Wolf Lammen, 12-Jul-2020.)
Assertion
Ref Expression
stdpc5v (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem stdpc5v
StepHypRef Expression
1 ax-5 2006 . 2 (𝜑 → ∀𝑥𝜑)
2 alim 1906 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
31, 2syl5 34 1 (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1651
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1905  ax-5 2006
This theorem is referenced by:  19.21v  2035  bj-ssb1a  33139  axc11next  39388
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