Axiom ax-frege1 42531

Description: The case in which 𝜑 is denied, 𝜓 is affirmed, and 𝜑 is affirmed is excluded. This is evident since 𝜑 cannot at the same time be denied and affirmed. Axiom 1 of [Frege1879] p. 26. Identical to ax-1 6. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-frege1	⊢ (𝜑 → (𝜓 → 𝜑))

Detailed syntax breakdown of Axiom ax-frege1

Step	Hyp	Ref	Expression
1		wph	. 2 wff 𝜑
2		wps	. . 3 wff 𝜓
3	2, 1	wi 4	. 2 wff (𝜓 → 𝜑)
4	1, 3	wi 4	1 wff (𝜑 → (𝜓 → 𝜑))

This axiom is referenced by:  rp-simp2-frege  42533  rp-frege3g  42535  frege3  42536  frege5  42541  rp-6frege  42544  frege26  42551  frege27  42552  frege11  42555  frege24  42556  frege36  42580