Theorem moabs 1041

Description: Absorption of existence condition by "at most one".

Assertion

Ref	Expression
moabs	|- (E*xph <-> (E.xph -> E*xph))

Proof of Theorem moabs

Step	Hyp	Ref	Expression
1		pm5.4 146	. 2 |- ((E.xph -> (E.xph -> E!xph)) <-> (E.xph -> E!xph))
2		df-mo 1010	. . 3 |- (E*xph <-> (E.xph -> E!xph))
3	2	imbi2i 160	. 2 |- ((E.xph -> E*xph) <-> (E.xph -> (E.xph -> E!xph)))
4	1, 3, 2	3bitr4r 159	1 |- (E*xph <-> (E.xph -> E*xph))

Syntax hints:   -> wi 2   <-> wb 127  E.wex 678  E!weu 1007  E*wmo 1008

This theorem is referenced by:  dffun6 2687

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-mo 1010

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