Theorem 19.23ad 1065

Description: Deduction from Theorem 19.23 of [Margaris] p. 90.

Hypotheses

Ref	Expression
19.23ad.1	|- (ph -> A.xph)
19.23ad.2	|- (ch -> A.xch)
19.23ad.3	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
19.23ad	|- (ph -> (E.xps -> ch))

Proof of Theorem 19.23ad

Step	Hyp	Ref	Expression
1		19.23ad.1	. . 3 |- (ph -> A.xph)
2		19.23ad.3	. . 3 |- (ph -> (ps -> ch))
3	1, 2	19.21ai 997	. 2 |- (ph -> A.x(ps -> ch))
4		19.23ad.2	. . 3 |- (ch -> A.xch)
5	4	19.23 1062	. 2 |- (A.x(ps -> ch) <-> (E.xps -> ch))
6	3, 5	sylib 198	1 |- (ph -> (E.xps -> ch))

Syntax hints:   -> wi 3  A.wal 953  E.wex 979

This theorem is referenced by:  19.23adv 1213  equs5 1220  a12study 1377  a12studyALT 1378  r19.23ad 1743  csbie2t 2030  mosubopt 2800  dffun7 3536  fopab2 3818  cbvfo 3880  tz7.48-1 3951  qusp 10489

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 962  ax-4 972  ax-5o 974  ax-6o 977

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980

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