Theorem bnj551

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Assertion	bnj551	$$⊢\left(m=\mathrm{suc}p\wedge m=\mathrm{suc}i\right)\to p=i$$

Proof

Step	Hyp	Ref	Expression
1		eqtr2	$$⊢\left(m=\mathrm{suc}p\wedge m=\mathrm{suc}i\right)\to \mathrm{suc}p=\mathrm{suc}i$$
2		suc11reg	$$⊢\mathrm{suc}p=\mathrm{suc}i\leftrightarrow p=i$$
3	1 2	sylib	$$⊢\left(m=\mathrm{suc}p\wedge m=\mathrm{suc}i\right)\to p=i$$