Theorem 2moex 1060

Description: Double quantification with "at most one".

Assertion

Ref	Expression
2moex	⊢ (∃*x∃yφ → ∀y∃*xφ)

Proof of Theorem 2moex

Step	Hyp	Ref	Expression
1		hbe1 709	. . 3 ⊢ (∃yφ → ∀y∃yφ)
2	1	hbmo 1033	. 2 ⊢ (∃*x∃yφ → ∀y∃*x∃yφ)
3		immo 1043	. . 3 ⊢ (∀x(φ → ∃yφ) → (∃*x∃yφ → ∃*xφ))
4		19.8a 712	. . 3 ⊢ (φ → ∃yφ)
5	3, 4	mpg 684	. 2 ⊢ (∃*x∃yφ → ∃*xφ)
6	2, 5	19.21ai 740	1 ⊢ (∃*x∃yφ → ∀y∃*xφ)

Syntax hints:   → wi 2  ∀wal 672  ∃wex 678  ∃*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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