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Metamath Proof Explorer

Theorem lttr

Description: Alias for axlttrn , for naming consistency with lttri . New proofs should generally use this instead of ax-pre-lttrn . (Contributed by NM, 10-Mar-2008)

		Ref	Expression
	Assertion	lttr	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ ) → ( ( 𝐴 < 𝐵 ∧ 𝐵 < 𝐶 ) → 𝐴 < 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		axlttrn	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ ) → ( ( 𝐴 < 𝐵 ∧ 𝐵 < 𝐶 ) → 𝐴 < 𝐶 ) )