Theorem bnj219

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

	Ref	Expression
Assertion	bnj219	⊢ ( 𝑛 = suc 𝑚 → 𝑚 E 𝑛 )

Proof

Step	Hyp	Ref	Expression
1		vex	⊢ 𝑚 ∈ V
2	1	bnj216	⊢ ( 𝑛 = suc 𝑚 → 𝑚 ∈ 𝑛 )
3		epel	⊢ ( 𝑚 E 𝑛 ↔ 𝑚 ∈ 𝑛 )
4	2 3	sylibr	⊢ ( 𝑛 = suc 𝑚 → 𝑚 E 𝑛 )