Axiom ax-frege58a 37189

Description: If ∀𝑥𝜑 is affirmed, [𝑦 / 𝑥]𝜑 cannot be denied. Identical to stdpc4 2341. Axiom 58 of [Frege1879] p. 51. (Contributed by RP, 28-Mar-2020.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-frege58a	⊢ ((𝜓 ∧ 𝜒) → if-(𝜑, 𝜓, 𝜒))

Detailed syntax breakdown of Axiom ax-frege58a

Step	Hyp	Ref	Expression
1		wps	. . 3 wff 𝜓
2		wch	. . 3 wff 𝜒
3	1, 2	wa 383	. 2 wff (𝜓 ∧ 𝜒)
4		wph	. . 3 wff 𝜑
5	4, 1, 2	wif 1006	. 2 wff if-(𝜑, 𝜓, 𝜒)
6	3, 5	wi 4	1 wff ((𝜓 ∧ 𝜒) → if-(𝜑, 𝜓, 𝜒))

This axiom is referenced by:  frege58acor  37190  frege61a  37193  frege67a  37199