Theorem bj-stdpc5 37832

Description: More direct proof of stdpc5 2244. (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 37831	. 2 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))

This proof depends on syntax axioms:   → wi 4  ∀wal 1567  Ⅎwnf 1815

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-12 2212

This proof depends on definitions:  df-bi 210  df-ex 1812  df-nf 1816

This theorem is used by: (None)