Theorem entr

Description: Transitivity of equinumerosity. Theorem 3 of Suppes p. 92. (Contributed by NM, 9-Jun-1998)

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

Proof

Step	Hyp	Ref	Expression
1		ener	$$⊢\approx \mathrm{Er}\mathrm{V}$$
2	1	a1i	$$⊢\top \to \approx \mathrm{Er}\mathrm{V}$$
3	2	ertr	$$⊢\top \to \left(\left(A\approx B\wedge B\approx C\right)\to A\approx C\right)$$
4	3	mptru	$$⊢\left(A\approx B\wedge B\approx C\right)\to A\approx C$$