Theorem 1t1e1ALT

Description: Alternate proof of 1t1e1 using a different set of axioms (add ax-mulrcl , ax-i2m1 , ax-1ne0 , ax-rrecex and remove ax-resscn , ax-mulcom , ax-mulass , ax-distr ). (Contributed by Steven Nguyen, 20-Sep-2022) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	1t1e1ALT	⊢ ( 1 · 1 ) = 1

Proof

Step	Hyp	Ref	Expression
1		1re	⊢ 1 ∈ ℝ
2		ax-1rid	⊢ ( 1 ∈ ℝ → ( 1 · 1 ) = 1 )
3	1 2	ax-mp	⊢ ( 1 · 1 ) = 1