Theorem hbmo 1407

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 1006	. . 3 |- (E.yph -> A.xE.yph)
3	1	hbeu 1389	. . 3 |- (E!yph -> A.xE!yph)
4	2, 3	hbim 1007	. 2 |- ((E.yph -> E!yph) -> A.x(E.yph -> E!yph))
5		df-mo 1383	. 2 |- (E*yph <-> (E.yph -> E!yph))
6	5	albii 999	. 2 |- (A.xE*yph <-> A.x(E.yph -> E!yph))
7	4, 5, 6	3imtr4 219	1 |- (E*yph -> A.xE*yph)

Syntax hints:   -> wi 3  A.wal 954  E.wex 980  E!weu 1380  E*wmo 1381

This theorem is referenced by:  moexex 1438  2moex 1440  2euex 1441  2exeu 1446  mosubopt 2804  dffunmof 3530

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-eu 1382  df-mo 1383

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