Theorem stdpc5v 1854

Description: Version of stdpc5 2063 with a dv condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020.) Revised to shorten 19.21v 1855. (Revised by Wolf Lammen, 12-Jul-2020.)

Assertion

Ref	Expression
stdpc5v	⊢ (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))

Distinct variable group:   𝜑,𝑥

Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem stdpc5v

Step	Hyp	Ref	Expression
1		ax-5 1827	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2		alim 1729	. 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
3	1, 2	syl5 33	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1473

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1728  ax-5 1827

This theorem is referenced by:  19.21v  1855  bj-ssb1a  31821  axc11next  37629