Theorem albi 1564

Description: Theorem 19.15 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
albi	|- (A.x(ph <-> ps) -> (A.xph <-> A.xps))

Proof of Theorem albi

Step	Hyp	Ref	Expression
1		bi1 178	. . 3 |- ((ph <-> ps) -> (ph -> ps))
2	1	al2imi 1561	. 2 |- (A.x(ph <-> ps) -> (A.xph -> A.xps))
3		bi2 189	. . 3 |- ((ph <-> ps) -> (ps -> ph))
4	3	al2imi 1561	. 2 |- (A.x(ph <-> ps) -> (A.xps -> A.xph))
5	2, 4	impbid 183	1 |- (A.x(ph <-> ps) -> (A.xph <-> A.xps))

Syntax hints:   -> wi 4   <-> wb 176  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  albii  1566  albidh  1590  19.16  1860  19.17  1861  intmin4  3956  dfiin2g  4001