Theorem 2moex 1060

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 709	. . 3 |- (E.yph -> A.yE.yph)
2	1	hbmo 1033	. 2 |- (E*xE.yph -> A.yE*xE.yph)
3		immo 1043	. . 3 |- (A.x(ph -> E.yph) -> (E*xE.yph -> E*xph))
4		19.8a 712	. . 3 |- (ph -> E.yph)
5	3, 4	mpg 684	. 2 |- (E*xE.yph -> E*xph)
6	2, 5	19.21ai 740	1 |- (E*xE.yph -> A.yE*xph)

Syntax hints:   -> wi 2  A.wal 672  E.wex 678  E*wmo 1008

This theorem is referenced by:  2euex 1061  2eu2 1068  2eu5 1071

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-mo 1010

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