Theorem moexexv 2720

Description: "At most one" double quantification. Usage of this theorem is discouraged because it depends on ax-13 2386. Use the weaker moexexvw 2709 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 1911	. 2 ⊢ Ⅎ𝑦𝜑
2	1	moexex 2719	1 ⊢ ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦∃𝑥(𝜑 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ wa 398  ∀wal 1531  ∃wex 1776  ∃*wmo 2616

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-10 2141  ax-11 2156  ax-12 2172  ax-13 2386

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-mo 2618

This theorem is referenced by: (None)