Theorem 19.22 1039

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 94	. . . 4 |- ((ph -> ps) -> (-. ps -> -. ph))
2	1	19.20ii 995	. . 3 |- (A.x(ph -> ps) -> (A.x -. ps -> A.x -. ph))
3	2	con3d 95	. 2 |- (A.x(ph -> ps) -> (-. A.x -. ph -> -. A.x -. ps))
4		df-ex 981	. 2 |- (E.xph <-> -. A.x -. ph)
5		df-ex 981	. 2 |- (E.xps <-> -. A.x -. ps)
6	3, 4, 5	3imtr4g 553	1 |- (A.x(ph -> ps) -> (E.xph -> E.xps))

Syntax hints:  -. wn 2   -> wi 3  A.wal 954  E.wex 980

This theorem is referenced by:  19.22i 1040  19.18 1050  19.22d 1062  19.23 1063  19.25 1084  ax9o 1122  sbied 1195  mo 1393  2mo 1447  r19.22 1731  chsscm 9112

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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