Theorem moabs 1415

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		pm5.4 167	. 2 |- ((E.xph -> (E.xph -> E!xph)) <-> (E.xph -> E!xph))
2		df-mo 1383	. . 3 |- (E*xph <-> (E.xph -> E!xph))
3	2	imbi2i 185	. 2 |- ((E.xph -> E*xph) <-> (E.xph -> (E.xph -> E!xph)))
4	1, 3, 2	3bitr4r 184	1 |- (E*xph <-> (E.xph -> E*xph))

Syntax hints:   -> wi 3   <-> wb 146  E.wex 980  E!weu 1380  E*wmo 1381

This theorem is referenced by:  dffun6 3539

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-mo 1383

Copyright terms: Public domain