Theorem 2eu2ex 1063

Description: Double existential uniqueness.

Assertion

Ref	Expression
2eu2ex	⊢ (∃!x∃!yφ → ∃x∃yφ)

Proof of Theorem 2eu2ex

Step	Hyp	Ref	Expression
1		euex 1021	. 2 ⊢ (∃!x∃!yφ → ∃x∃!yφ)
2		euex 1021	. . 3 ⊢ (∃!yφ → ∃yφ)
3	2	19.22i 723	. 2 ⊢ (∃x∃!yφ → ∃x∃yφ)
4	1, 3	syl 12	1 ⊢ (∃!x∃!yφ → ∃x∃yφ)

Syntax hints:   → wi 2  ∃wex 678  ∃!weu 1007

This theorem is referenced by:  2eu1 1067

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

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