Theorem 19.38OLD 1874

Description: Obsolete proof of 19.38 as of 2-Jan-2018. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem 19.38OLD

Step	Hyp	Ref	Expression
1		nfe1 1732	. . 3 |- F/xE.xph
2		nfa1 1788	. . 3 |- F/xA.xps
3	1, 2	nfim 1813	. 2 |- F/x(E.xph -> A.xps)
4		19.8a 1756	. . 3 |- (ph -> E.xph)
5		sp 1747	. . 3 |- (A.xps -> ps)
6	4, 5	imim12i 53	. 2 |- ((E.xph -> A.xps) -> (ph -> ps))
7	3, 6	alrimi 1765	1 |- ((E.xph -> A.xps) -> A.x(ph -> ps))

Syntax hints:   -> wi 4  A.wal 1540  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)