Theorem eubi 26969

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 1719	. 2 |- F/ x A. x ( ph <-> ps )
2		ax-4 1692	. 2 |- ( A. x ( ph <-> ps ) -> ( ph <-> ps ) )
3	1, 2	eubid 2124	1 |- ( A. x ( ph <-> ps ) -> ( E! x ph <-> E! x ps ) )

Syntax hints:   -> wi 6   <-> wb 178   A.wal 1532   E!weu 2117

This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-4 1692

This theorem depends on definitions:  df-bi 179  df-ex 1538  df-nf 1540  df-eu 2121