Axiom ax-frege58b

Description: If A. x ph is affirmed, [ y / x ] ph cannot be denied. Identical to stdpc4 . Axiom 58 of Frege1879 p. 51. (Contributed by RP, 28-Mar-2020) (New usage is discouraged.)

	Ref	Expression
Assertion	ax-frege58b	⊢ ( ∀ 𝑥 𝜑 → [ 𝑦 / 𝑥 ] 𝜑 )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		vx	⊢ 𝑥
1		wph	⊢ 𝜑
2	1 0	wal	⊢ ∀ 𝑥 𝜑
3		vy	⊢ 𝑦
4	1 0 3	wsb	⊢ [ 𝑦 / 𝑥 ] 𝜑
5	2 4	wi	⊢ ( ∀ 𝑥 𝜑 → [ 𝑦 / 𝑥 ] 𝜑 )