Axiom ax-L7 19

Description: Axiom of Equality.

Assertion

Ref	Expression
ax-L7	⊢ (𝑡 = 𝑢 → (𝑡 = 𝑤 → 𝑢 = 𝑤))

Detailed syntax breakdown of Axiom ax-L7

Step	Hyp	Ref	Expression
1		term-t	. . 3 term 𝑡
2		term-u	. . 3 term 𝑢
3	1, 2	wff-equals 6	. 2 wff 𝑡 = 𝑢
4		term-w	. . . 4 term 𝑤
5	1, 4	wff-equals 6	. . 3 wff 𝑡 = 𝑤
6	2, 4	wff-equals 6	. . 3 wff 𝑢 = 𝑤
7	5, 6	wff-imp 10	. 2 wff (𝑡 = 𝑤 → 𝑢 = 𝑤)
8	3, 7	wff-imp 10	1 wff (𝑡 = 𝑢 → (𝑡 = 𝑤 → 𝑢 = 𝑤))

This axiom is referenced by:  eqref-P5  626  eqsym-P5  627  eqtrns-P5  630  subeql-P5  632  subeqr-P5-L1  634