Theorem bi2al 696

Description: Inference adding 2 universal quantifiers to both sides of an equivalence.

Hypothesis

Ref	Expression
bial.1	|- (ph <-> ps)

Assertion

Ref	Expression
bi2al	|- (A.xA.yph <-> A.xA.yps)

Proof of Theorem bi2al

Step	Hyp	Ref	Expression
1		bial.1	. . 3 |- (ph <-> ps)
2	1	bial 695	. 2 |- (A.yph <-> A.yps)
3	2	bial 695	1 |- (A.xA.yph <-> A.xA.yps)

Syntax hints:   <-> wb 127  A.wal 672

This theorem is referenced by:  hbsb4t 906  mo 1020  mo4f 1028  2eu4 1070  axac 1085  ralcom 1312  weinxp 2467  intasym 2627  dffun4 2676  fununi 2705  aceq0 3553  zfcndac 3765

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

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

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