Theorem 2moex 1480

Description: Double quantification with "at most one."

Assertion

Ref	Expression
2moex	|- (E*xE.yph -> A.yE*xph)

Proof of Theorem 2moex

Step	Hyp	Ref	Expression
1		hbe1 1052	. . 3 |- (E.yph -> A.yE.yph)
2	1	hbmo 1446	. 2 |- (E*xE.yph -> A.yE*xE.yph)
3		19.8a 1065	. . 3 |- (ph -> E.yph)
4	3	immoi 1457	. 2 |- (E*xE.yph -> E*xph)
5	2, 4	19.21ai 1034	1 |- (E*xE.yph -> A.yE*xph)

Syntax hints:   -> wi 3  A.wal 990  E.wex 1016  E*wmo 1420

This theorem is referenced by:  2euex 1481  2eu2 1490  2eu5 1493

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 998  ax-gen 999  ax-8 1000  ax-10 1002  ax-11 1003  ax-12 1004  ax-17 1007  ax-4 1009  ax-5o 1011  ax-6o 1014  ax-9o 1159  ax-10o 1177  ax-16 1247  ax-11o 1255

This theorem depends on definitions:  df-bi 145  df-or 222  df-an 223  df-ex 1017  df-sb 1209  df-eu 1421  df-mo 1422

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