Theorem bj-stdpc5 34151

Description: More direct proof of stdpc5 2208. (Contributed by BJ, 15-Sep-2018.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-stdpc5.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
bj-stdpc5	⊢ (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))

Proof of Theorem bj-stdpc5

Step	Hyp	Ref	Expression
1		bj-stdpc5.1	. 2 ⊢ Ⅎ𝑥𝜑
2		stdpc5t 34150	. 2 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1535  Ⅎwnf 1784

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2177

This theorem depends on definitions:  df-bi 209  df-ex 1781  df-nf 1785

This theorem is referenced by: (None)