Theorem 19.22 722

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

Assertion

Ref	Expression
19.22	|- (A.x(ph -> ps) -> (E.xph -> E.xps))

Proof of Theorem 19.22

Step	Hyp	Ref	Expression
1		con3 86	. . . 4 |- ((ph -> ps) -> (-. ps -> -. ph))
2	1	19.20ii 692	. . 3 |- (A.x(ph -> ps) -> (A.x -. ps -> A.x -. ph))
3	2	con3d 87	. 2 |- (A.x(ph -> ps) -> (-. A.x -. ph -> -. A.x -. ps))
4		df-ex 679	. 2 |- (E.xph <-> -. A.x -. ph)
5		df-ex 679	. 2 |- (E.xps <-> -. A.x -. ps)
6	3, 4, 5	3imtr4g 426	1 |- (A.x(ph -> ps) -> (E.xph -> E.xps))

Syntax hints:  -. wn 1   -> wi 2  A.wal 672  E.wex 678

This theorem is referenced by:  19.22i 723  19.18 732  19.22d 744  19.23 745  19.25 763  ax9 807  sbied 903  mo 1020  r19.22 1272  chsscm 5147

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-gen 677

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

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