Theorem 19.20 1035

Description: Theorem 19.20 of [Margaris] p. 90. (The proof was shortened by O'Cat, 30-Mar-2008.)

Assertion

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

Proof of Theorem 19.20

Step	Hyp	Ref	Expression
1		id 59	. . . 4 |- ((ph -> ps) -> (ph -> ps))
2	1	a4sd 1026	. . 3 |- ((ph -> ps) -> (A.xph -> ps))
3	2	19.20i 1033	. 2 |- (A.x(ph -> ps) -> A.x(A.xph -> ps))
4		ax-5o 1016	. 2 |- (A.x(A.xph -> ps) -> (A.xph -> A.xps))
5	3, 4	syl 10	1 |- (A.x(ph -> ps) -> (A.xph -> A.xps))

Syntax hints:   -> wi 3  A.wal 995

This theorem is referenced by:  19.20ii 1036  19.21 1097  19.29 1112  19.30 1126  19.21t 1156  sbal1 1388  mo 1435  2mo 1490

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

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