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Metamath Proof Explorer

Theorem bj-stdpc5t

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

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

Proof

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