Theorem 2moex 1443

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 1018	. . 3 |- (E.yph -> A.yE.yph)
2	1	hbmo 1409	. 2 |- (E*xE.yph -> A.yE*xE.yph)
3		19.8a 1031	. . 3 |- (ph -> E.yph)
4	3	immoi 1420	. 2 |- (E*xE.yph -> E*xph)
5	2, 4	19.21ai 1000	1 |- (E*xE.yph -> A.yE*xph)

Syntax hints:   -> wi 3  A.wal 956  E.wex 982  E*wmo 1383

This theorem is referenced by:  2euex 1444  2eu2 1453  2eu5 1456

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385

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