Theorem 19.22 1080

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 98	. . . 4 |- ((ph -> ps) -> (-. ps -> -. ph))
2	1	19.20ii 1036	. . 3 |- (A.x(ph -> ps) -> (A.x -. ps -> A.x -. ph))
3	2	con3d 99	. 2 |- (A.x(ph -> ps) -> (-. A.x -. ph -> -. A.x -. ps))
4		df-ex 1022	. 2 |- (E.xph <-> -. A.x -. ph)
5		df-ex 1022	. 2 |- (E.xps <-> -. A.x -. ps)
6	3, 4, 5	3imtr4g 564	1 |- (A.x(ph -> ps) -> (E.xph -> E.xps))

Syntax hints:  -. wn 2   -> wi 3  A.wal 995  E.wex 1021

This theorem is referenced by:  19.22i 1081  19.18 1091  19.22d 1103  19.23 1104  19.25 1125  ax9o 1163  sbied 1237  mo 1435  2mo 1490  r19.22 1778  chsscmi 9195

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1004  ax-4 1014  ax-5o 1016

This theorem depends on definitions:  df-bi 154  df-an 232  df-ex 1022

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