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	⊢ ( ( 𝑚 = suc 𝑝 ∧ 𝑚 = suc 𝑖 ) → 𝑝 = 𝑖 )

Proof

Step	Hyp	Ref	Expression
1		eqtr2	⊢ ( ( 𝑚 = suc 𝑝 ∧ 𝑚 = suc 𝑖 ) → suc 𝑝 = suc 𝑖 )
2		suc11reg	⊢ ( suc 𝑝 = suc 𝑖 ↔ 𝑝 = 𝑖 )
3	1 2	sylib	⊢ ( ( 𝑚 = suc 𝑝 ∧ 𝑚 = suc 𝑖 ) → 𝑝 = 𝑖 )