Theorem 19.38 1077

Description: Theorem 19.38 of [Margaris] p. 90.

Assertion

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

Proof of Theorem 19.38

Step	Hyp	Ref	Expression
1		hbe1 1012	. . 3 |- (E.xph -> A.xE.xph)
2		hba1 1000	. . 3 |- (A.xps -> A.xA.xps)
3	1, 2	hbim 1004	. 2 |- ((E.xph -> A.xps) -> A.x(E.xph -> A.xps))
4		19.8a 1025	. . 3 |- (ph -> E.xph)
5		ax-4 970	. . 3 |- (A.xps -> ps)
6	4, 5	imim12i 18	. 2 |- ((E.xph -> A.xps) -> (ph -> ps))
7	3, 6	19.21ai 995	1 |- ((E.xph -> A.xps) -> A.x(ph -> ps))

Syntax hints:   -> wi 3  A.wal 951  E.wex 977

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972  ax-6o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978

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