Theorem eubi 16402

Description: Theorem *14.271 in [WhiteheadRussell] p. 192.

Assertion

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

Proof of Theorem eubi

Step	Hyp	Ref	Expression
1		hba1 1350	. 2 |- (A.x(ph <-> ps) -> A.xA.x(ph <-> ps))
2		ax-4 1319	. 2 |- (A.x(ph <-> ps) -> (ph <-> ps))
3	1, 2	eubid 1778	1 |- (A.x(ph <-> ps) -> (E!xph <-> E!xps))

Syntax hints:   -> wi 3   <-> wb 163  A.wal 1296  E!weu 1771

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-17 1317  ax-4 1319  ax-5o 1321

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-eu 1775

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