Axiom ax-frege58b 38195

Description: If A. x ph is affirmed, [ y / x ] ph cannot be denied. Identical to stdpc4 2353. Axiom 58 of [Frege1879] p. 51. (Contributed by RP, 28-Mar-2020.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-frege58b	|- ( A. x ph -> [ y / x ] ph )

Detailed syntax breakdown of Axiom ax-frege58b

Step	Hyp	Ref	Expression
1		wph	. . 3 wff ph
2		vx	. . 3 setvar x
3	1, 2	wal 1481	. 2 wff A. x ph
4		vy	. . 3 setvar y
5	1, 2, 4	wsb 1880	. 2 wff [ y / x ] ph
6	3, 5	wi 4	1 wff ( A. x ph -> [ y / x ] ph )

This axiom is referenced by:  frege58bid  38196  frege58bcor  38197  frege60b  38199  frege61b  38200  frege67b  38206  frege58c  38215