Theorem 2moex 1417

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 990	. . 3 |- (E.yph -> A.yE.yph)
2	1	hbmo 1384	. 2 |- (E*xE.yph -> A.yE*xE.yph)
3		19.8a 1005	. . 3 |- (ph -> E.yph)
4	3	immoi 1395	. 2 |- (E*xE.yph -> E*xph)
5	2, 4	19.21ai 974	1 |- (E*xE.yph -> A.yE*xph)

Syntax hints:   -> wi 3  A.wal 950  E.wex 956  E*wmo 1358

This theorem is referenced by:  2euex 1418  2eu2 1427  2eu5 1430

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-7 954  ax-gen 955  ax-8 1101  ax-9 1102  ax-10 1103  ax-12 1104  ax-11 1180  ax-17 1190  ax-16 1194  ax-11o 1202

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 957  df-sb 1155  df-eu 1359  df-mo 1360

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