Theorem sdomentr

Description: Transitivity of strict dominance and equinumerosity. Exercise 11 of Suppes p. 98. (Contributed by NM, 26-Oct-2003)

	Ref	Expression
Assertion	sdomentr	$$⊢\left(A\prec B\wedge B\approx C\right)\to A\prec C$$

Proof

Step	Hyp	Ref	Expression
1		endom	$$⊢B\approx C\to B\preccurlyeq C$$
2		sdomdomtr	$$⊢\left(A\prec B\wedge B\preccurlyeq C\right)\to A\prec C$$
3	1 2	sylan2	$$⊢\left(A\prec B\wedge B\approx C\right)\to A\prec C$$