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Theorem bj-stdpc5 34266
Description: More direct proof of stdpc5 2206. (Contributed by BJ, 15-Sep-2018.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-stdpc5.1 𝑥𝜑
Assertion
Ref Expression
bj-stdpc5 (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓))

Proof of Theorem bj-stdpc5
StepHypRef Expression
1 bj-stdpc5.1 . 2 𝑥𝜑
2 stdpc5t 34265 . 2 (Ⅎ𝑥𝜑 → (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓)))
31, 2ax-mp 5 1 (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536  wnf 1785
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2175
This theorem depends on definitions:  df-bi 210  df-ex 1782  df-nf 1786
This theorem is referenced by: (None)
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