Theorem moexexv 2669

Description: "At most one" double quantification. Usage of this theorem is discouraged because it depends on ax-13 2406. Use the weaker moexexvw 2658 when possible. (Contributed by NM, 26-Jan-1997.) (New usage is discouraged.)

Assertion

Ref	Expression
moexexv	⊢ ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦∃𝑥(𝜑 ∧ 𝜓))

Distinct variable group:   𝜑,𝑦

Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑥, 𝑦)

Proof of Theorem moexexv

Step	Hyp	Ref	Expression
1		nfv 1947	. 2 ⊢ Ⅎ𝑦𝜑
2	1	moexex 2668	1 ⊢ ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦∃𝑥(𝜑 ∧ 𝜓))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401  ∀wal 1568  ∃wex 1812  ∃*wmo 2567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-10 2179  ax-11 2195  ax-12 2216  ax-13 2406

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-nf 1817  df-mo 2569

This theorem is used by: (None)