Metamath Proof Explorer

Theorem 2exbii

Description: Inference adding two existential quantifiers to both sides of an equivalence. (Contributed by NM, 16-Mar-1995)

Ref Expression
Hypothesis 2exbii.1 
|- ( ph <-> ps )
Assertion 2exbii 
|- ( E. x E. y ph <-> E. x E. y ps )

Proof

Step Hyp Ref Expression
1 2exbii.1 
 |-  ( ph <-> ps )
2 1 exbii 
 |-  ( E. y ph <-> E. y ps )
3 2 exbii 
 |-  ( E. x E. y ph <-> E. x E. y ps )