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Metamath Proof Explorer

Theorem 19.23vv

Description: Theorem 19.23v extended to two variables. (Contributed by NM, 10-Aug-2004)

Ref Expression
Assertion 19.23vv 
|- ( A. x A. y ( ph -> ps ) <-> ( E. x E. y ph -> ps ) )

Proof

Step Hyp Ref Expression
1 19.23v 
 |-  ( A. y ( ph -> ps ) <-> ( E. y ph -> ps ) )
2 1 albii 
 |-  ( A. x A. y ( ph -> ps ) <-> A. x ( E. y ph -> ps ) )
3 19.23v 
 |-  ( A. x ( E. y ph -> ps ) <-> ( E. x E. y ph -> ps ) )
4 2 3 bitri 
 |-  ( A. x A. y ( ph -> ps ) <-> ( E. x E. y ph -> ps ) )