Theorem 2moex 1433

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 1012	. . 3 ⊢ (∃yφ → ∀y∃yφ)
2	1	hbmo 1400	. 2 ⊢ (∃*x∃yφ → ∀y∃*x∃yφ)
3		19.8a 1025	. . 3 ⊢ (φ → ∃yφ)
4	3	immoi 1411	. 2 ⊢ (∃*x∃yφ → ∃*xφ)
5	2, 4	19.21ai 995	1 ⊢ (∃*x∃yφ → ∀y∃*xφ)

Syntax hints:   → wi 3  ∀wal 951  ∃wex 977  ∃*wmo 1374

This theorem is referenced by:  2euex 1434  2eu2 1443  2eu5 1446

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376

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