Theorem moexexv 2274

Description: "At most one" double quantification. (Contributed by NM, 26-Jan-1997.)

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 1619	. 2 ⊢ Ⅎyφ
2	1	moexex 2273	1 ⊢ ((∃*xφ ∧ ∀x∃*yψ) → ∃*y∃x(φ ∧ ψ))

Syntax hints:   → wi 4   ∧ wa 358  ∀wal 1540  ∃wex 1541  ∃*wmo 2205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209

This theorem is referenced by:  mosub  3014  funco  5142