Theorem moexexv 2680

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 1992	. 2 ⊢ Ⅎ𝑦𝜑
2	1	moexex 2679	1 ⊢ ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦∃𝑥(𝜑 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ wa 383  ∀wal 1630  ∃wex 1853  ∃*wmo 2608

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-eu 2611  df-mo 2612

This theorem is referenced by:  mosub  3525  funco  6089