Theorem bj-stdpc5t 36769

Description: Alias of bj-nnf-alrim 36756 for labeling consistency (a standard predicate calculus axiom). Closed form of stdpc5 2208 proved from modalK (obsoleting stdpc5v 1938). (Contributed by BJ, 2-Dec-2023.) Use bj-nnf-alrim 36756 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 36756	1 ⊢ (Ⅎ'𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓)))

Syntax hints:   → wi 4  ∀wal 1538  Ⅎ'wnnf 36724

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 1809

This theorem depends on definitions:  df-bi 207  df-an 396  df-bj-nnf 36725

This theorem is referenced by: (None)