Metamath Proof Explorer

Theorem bnj216

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

Ref Expression
Hypothesis bnj216.1 
|- B e. _V
Assertion bnj216 
|- ( A = suc B -> B e. A )

Proof

Step Hyp Ref Expression
1 bnj216.1 
 |-  B e. _V
2 1 sucid 
 |-  B e. suc B
3 eleq2 
 |-  ( A = suc B -> ( B e. A <-> B e. suc B ) )
4 2 3 mpbiri 
 |-  ( A = suc B -> B e. A )