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Metamath Proof Explorer

Theorem 19.44

Description: Theorem 19.44 of Margaris p. 90. See 19.44v for a version requiring fewer axioms. (Contributed by NM, 12-Mar-1993)

Ref Expression
Hypothesis 19.44.1 
|- F/ x ps
Assertion 19.44 
|- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ ps ) )

Proof

Step Hyp Ref Expression
1 19.44.1 
 |-  F/ x ps
2 19.43 
 |-  ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
3 1 19.9 
 |-  ( E. x ps <-> ps )
4 3 orbi2i 
 |-  ( ( E. x ph \/ E. x ps ) <-> ( E. x ph \/ ps ) )
5 2 4 bitri 
 |-  ( E. x ( ph \/ ps ) <-> ( E. x ph \/ ps ) )