Theorem moexexv 2542

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

Assertion

Ref	Expression
moexexv	|- ( ( E* x ph /\ A. x E* y ps ) -> E* y E. x ( ph /\ ps ) )

Distinct variable group:   ph, y

Allowed substitution hints:   ph( x)   ps( x, y)

Proof of Theorem moexexv

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ y ph
2	1	moexex 2541	1 |- ( ( E* x ph /\ A. x E* y ps ) -> E* y E. x ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 384   A.wal 1481   E.wex 1704   E*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475

This theorem is referenced by:  mosub  3384  funco  5928