Theorem bj-stdpc5t 37412

Description: Alias of bj-nnf-alrim 37411 for labeling consistency (a standard predicate calculus axiom). Closed form of stdpc5 2247 proved from modalK (obsoleting stdpc5v 1971). (Contributed by BJ, 2-Dec-2023.) Use bj-nnf-alrim 37411 instead. (New usaged is discouraged.)

Assertion

Ref	Expression
bj-stdpc5t	⊢ (Ⅎ'𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓)))

Proof of Theorem bj-stdpc5t

Step	Hyp	Ref	Expression
1		bj-nnf-alrim 37411	1 ⊢ (Ⅎ'𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓)))

This proof depends on syntax axioms:   → wi 4  ∀wal 1568  Ⅎ'wnnf 37392

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 1842

This proof depends on definitions:  df-bi 210  df-an 402  df-bj-nnf 37393

This theorem is used by: (None)