Theorem moabs 2248

Description: Absorption of existence condition by "at most one." (Contributed by NM, 4-Nov-2002.)

Assertion

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

Proof of Theorem moabs

Step	Hyp	Ref	Expression
1		pm5.4 351	. 2 |- ((E.xph -> (E.xph -> E!xph)) <-> (E.xph -> E!xph))
2		df-mo 2209	. . 3 |- (E*xph <-> (E.xph -> E!xph))
3	2	imbi2i 303	. 2 |- ((E.xph -> E*xph) <-> (E.xph -> (E.xph -> E!xph)))
4	1, 3, 2	3bitr4ri 269	1 |- (E*xph <-> (E.xph -> E*xph))

Syntax hints:   -> wi 4   <-> wb 176  E.wex 1541  E!weu 2204  E*wmo 2205

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177  df-mo 2209

This theorem is referenced by:  dffun7  5133