Theorem 19.22d 1060

Description: Deduction from Theorem 19.22 of [Margaris] p. 90.

Hypotheses

Ref	Expression
19.22d.1	|- (ph -> A.xph)
19.22d.2	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
19.22d	|- (ph -> (E.xps -> E.xch))

Proof of Theorem 19.22d

Step	Hyp	Ref	Expression
1		19.22d.1	. . 3 |- (ph -> A.xph)
2		19.22d.2	. . 3 |- (ph -> (ps -> ch))
3	1, 2	19.21ai 996	. 2 |- (ph -> A.x(ps -> ch))
4		19.22 1037	. 2 |- (A.x(ps -> ch) -> (E.xps -> E.xch))
5	3, 4	syl 10	1 |- (ph -> (E.xps -> E.xch))

Syntax hints:   -> wi 3  A.wal 952  E.wex 978

This theorem is referenced by:  hbexd 1112  exintr 1115  equvini 1166  19.22dv 1288  mopick2 1434  ssopab2 2817  dmcosseq 3357  axextnd 4923  axpowndlem3 4931  axregndlem1 4934  axregnd 4936  suppsr2 5203

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-4 971  ax-5o 973

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979

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