Theorem 19.9d 1013

Description: A deduction version of one direction of 19.9 1012.

Hypotheses

Ref	Expression
19.9d.1	|- (ps -> A.xps)
19.9d.2	|- (ps -> (ph -> A.xph))

Assertion

Ref	Expression
19.9d	|- (ps -> (E.xph -> ph))

Proof of Theorem 19.9d

Step	Hyp	Ref	Expression
1		19.9d.1	. 2 |- (ps -> A.xps)
2		19.9d.2	. . 3 |- (ps -> (ph -> A.xph))
3	2	19.20i 968	. 2 |- (A.xps -> A.x(ph -> A.xph))
4		19.9t 1011	. 2 |- (A.x(ph -> A.xph) -> (E.xph -> ph))
5	1, 3, 4	3syl 20	1 |- (ps -> (E.xph -> ph))

Syntax hints:   -> wi 3  A.wal 950  E.wex 956

This theorem is referenced by:  sbequi 1212

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-gen 955

This theorem depends on definitions:  df-bi 147  df-ex 957

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