Theorem eubi 27508

Description: Theorem *14.271 in [WhiteheadRussell] p. 192. (Contributed by Andrew Salmon, 11-Jul-2011.)

Assertion

Ref	Expression
eubi	|- ( A. x ( ph <-> ps ) -> ( E! x ph <-> E! x ps ) )

Proof of Theorem eubi

Step	Hyp	Ref	Expression
1		nfa1 1802	. 2 |- F/ x A. x ( ph <-> ps )
2		sp 1759	. 2 |- ( A. x ( ph <-> ps ) -> ( ph <-> ps ) )
3	1, 2	eubid 2265	1 |- ( A. x ( ph <-> ps ) -> ( E! x ph <-> E! x ps ) )

Syntax hints:   -> wi 4   <-> wb 177   A.wal 1546   E!weu 2258

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757

This theorem depends on definitions:  df-bi 178  df-ex 1548  df-nf 1551  df-eu 2262