Theorem spv 1737

Description: Specialization, using implicit substitition. (Contributed by NM, 30-Aug-1993.)

Hypothesis

Ref	Expression
spv.1	|- (x = y -> (ph <-> ps))

Assertion

Ref	Expression
spv	|- (A.xph -> ps)

Distinct variable group:   ps,x

Allowed substitution hints:   ph(x,y)   ps(y)

Proof of Theorem spv

Step	Hyp	Ref	Expression
1		spv.1	. . 3 |- (x = y -> (ph <-> ps))
2	1	biimpd 132	. 2 |- (x = y -> (ph -> ps))
3	2	spimv 1689	1 |- (A.xph -> ps)

Syntax hints:   -> wi 4   <-> wb 98  A.wal 1240

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424

This theorem depends on definitions:  df-bi 110  df-nf 1347

This theorem is referenced by:  chvarv  1809  ru  2757  nalset  3878  tfisi  4253  bj-nalset  9350