Theorem ralimiaa 2167

Description: Inference quantifying both antecedent and consequent.

Hypothesis

Ref	Expression
ralimiaa.1	|- ((x e. A /\ ph) -> ps)

Assertion

Ref	Expression
ralimiaa	|- (A.x e. A ph -> A.x e. A ps)

Proof of Theorem ralimiaa

Step	Hyp	Ref	Expression
1		ralimiaa.1	. . 3 |- ((x e. A /\ ph) -> ps)
2	1	ex 402	. 2 |- (x e. A -> (ph -> ps))
3	2	ralimia 2166	1 |- (A.x e. A ph -> A.x e. A ps)

Syntax hints:   -> wi 3   /\ wa 240   e. wcel 1300  A.wral 2105

This theorem is referenced by:  tz7.48-2 5166  serzcmp0 8315  climsub 8390  bcthlem30 9306  riesz4i 11633  dmdbr6ati 11995  srefwref 14373  taralt 15211  tartarmap 15265

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

This theorem depends on definitions:  df-bi 164  df-an 242  df-ral 2109

Copyright terms: Public domain