Theorem biraldva 1215

Description: Formula-building rule for restricted universal quantifier (deduction rule).

Hypothesis

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

Assertion

Ref	Expression
biraldva	|- (ph -> (A.x e. A ps <-> A.x e. A ch))

Distinct variable group(s):   ph,x

Proof of Theorem biraldva

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 |- (ph -> A.xph)
2		biraldva.1	. 2 |- ((ph /\ x e. A) -> (ps <-> ch))
3	1, 2	biralda 1213	1 |- (ph -> (A.x e. A ps <-> A.x e. A ch))

Syntax hints:   -> wi 2   <-> wb 127   /\ wa 196   e. wcel 1092  A.wral 1201

This theorem is referenced by:  ordunisssuc 2334  tfindsg2 2403  weinxp 2467  f1oweOLD 2944  isfinite2 3437  kmlem2 3581  iscard 3659  sup3 4511  indstr 4611  mdbr2 5728  dmdbr2 5733

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-an 198  df-ral 1205

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