This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 19.45

Description: Theorem 19.45 of Margaris p. 90. See 19.45v for a version requiring fewer axioms. (Contributed by NM, 12-Mar-1993)

Ref Expression
Hypothesis 19.45.1 
|- F/ x ph
Assertion 19.45 
|- ( E. x ( ph \/ ps ) <-> ( ph \/ E. x ps ) )

Proof

Step Hyp Ref Expression
1 19.45.1 
 |-  F/ x ph
2 19.43 
 |-  ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
3 1 19.9 
 |-  ( E. x ph <-> ph )
4 3 orbi1i 
 |-  ( ( E. x ph \/ E. x ps ) <-> ( ph \/ E. x ps ) )
5 2 4 bitri 
 |-  ( E. x ( ph \/ ps ) <-> ( ph \/ E. x ps ) )