Theorem hbmo1 1032

Description: Bound-variable hypothesis builder for "at most one".

Assertion

Ref	Expression
hbmo1	|- (E*xph -> A.xE*xph)

Proof of Theorem hbmo1

Step	Hyp	Ref	Expression
1		hbe1 709	. . 3 |- (E.xph -> A.xE.xph)
2		hbeu1 1015	. . 3 |- (E!xph -> A.xE!xph)
3	1, 2	hbim 702	. 2 |- ((E.xph -> E!xph) -> A.x(E.xph -> E!xph))
4		df-mo 1010	. 2 |- (E*xph <-> (E.xph -> E!xph))
5	4	bial 695	. 2 |- (A.xE*xph <-> A.x(E.xph -> E!xph))
6	3, 4, 5	3imtr4 192	1 |- (E*xph -> A.xE*xph)

Syntax hints:   -> wi 2  A.wal 672  E.wex 678  E!weu 1007  E*wmo 1008

This theorem is referenced by:  mopick2 1057  moexex 1058  2eu3 1069

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-eu 1009  df-mo 1010

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