Theorem a4b1 928

Description: Infer specialization rule from substitution instance.

Hypothesis

Ref	Expression
a4b1.1	|- (x = y -> (ph <-> ps))

Assertion

Ref	Expression
a4b1	|- (A.xph -> ps)

Distinct variable group(s):   ps,x

Proof of Theorem a4b1

Step	Hyp	Ref	Expression
1		a4b1.1	. . 3 |- (x = y -> (ph <-> ps))
2	1	biimpd 135	. 2 |- (x = y -> (ph -> ps))
3	2	a4b 927	1 |- (A.xph -> ps)

Syntax hints:   -> wi 2   <-> wb 127  A.wal 672   = weq 797

This theorem is referenced by:  chv 984  ru 1437  nalset 1482  setind 3492  karden 3551  prlem934a 3931  suppsr2 4017  peano2nn 4433

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-6 675  ax-gen 677  ax-9 799  ax-17 925

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

metamath.org