Axiom ax-frege58b 44704

Description: If ∀𝑥𝜑 is affirmed, [𝑦 / 𝑥]𝜑 cannot be denied. Identical to stdpc4 2105. Axiom 58 of [Frege1879] p. 51. (Contributed by RP, 28-Mar-2020.) (New usage is discouraged.)

Assertion

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

Detailed syntax breakdown of Axiom ax-frege58b

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		vx	. . 3 setvar 𝑥
3	1, 2	wal 1568	. 2 wff ∀𝑥𝜑
4		vy	. . 3 setvar 𝑦
5	1, 2, 4	wsb 2099	. 2 wff [𝑦 / 𝑥]𝜑
6	3, 5	wi 4	1 wff (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)

This axiom is used by:  frege58bid  44705  frege58bcor  44706  frege60b  44708  frege61b  44709  frege67b  44715  frege58c  44724