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Metamath Proof Explorer

Theorem 19.44v

Description: Version of 19.44 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion 19.44v 
|- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ ps ) )

Proof

Step Hyp Ref Expression
1 19.43 
 |-  ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
2 19.9v 
 |-  ( E. x ps <-> ps )
3 2 orbi2i 
 |-  ( ( E. x ph \/ E. x ps ) <-> ( E. x ph \/ ps ) )
4 1 3 bitri 
 |-  ( E. x ( ph \/ ps ) <-> ( E. x ph \/ ps ) )