Theorem hbmo 1803

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

Hypothesis

Ref	Expression
hbmo.1	|- (ph -> A.xph)

Assertion

Ref	Expression
hbmo	|- (E*yph -> A.xE*yph)

Proof of Theorem hbmo

Step	Hyp	Ref	Expression
1		hbmo.1	. . . 4 |- (ph -> A.xph)
2	1	hbex 1353	. . 3 |- (E.yph -> A.xE.yph)
3	1	hbeu 1782	. . 3 |- (E!yph -> A.xE!yph)
4	2, 3	hbim 1354	. 2 |- ((E.yph -> E!yph) -> A.x(E.yph -> E!yph))
5		df-mo 1776	. 2 |- (E*yph <-> (E.yph -> E!yph))
6	5	albii 1346	. 2 |- (A.xE*yph <-> A.x(E.yph -> E!yph))
7	4, 5, 6	3imtr4i 236	1 |- (E*yph -> A.xE*yph)

Syntax hints:   -> wi 3  A.wal 1296  E.wex 1326  E!weu 1771  E*wmo 1772

This theorem is referenced by:  moexex 1841  2moex 1843  2euex 1844  2euexOLD 1845  2exeu 1850  mosubopt 3551  dffun6f 4435

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-10 1308  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-eu 1775  df-mo 1776

Copyright terms: Public domain