Theorem 19.38 760

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 709	. . 3 |- (E.xph -> A.xE.xph)
2		hba1 698	. . 3 |- (A.xps -> A.xA.xps)
3	1, 2	hbim 702	. 2 |- ((E.xph -> A.xps) -> A.x(E.xph -> A.xps))
4		19.8a 712	. . 3 |- (ph -> E.xph)
5		ax-4 673	. . 3 |- (A.xps -> ps)
6	4, 5	syl34 20	. 2 |- ((E.xph -> A.xps) -> (ph -> ps))
7	3, 6	19.21ai 740	1 |- ((E.xph -> A.xps) -> A.x(ph -> ps))

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

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-6 675  ax-gen 677

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

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