Theorem 19.22dvv 949

Description: Deduction from Theorem 19.22 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.20dvv.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
19.22dvv	|- (ph -> (E.xE.yps -> E.xE.ych))

Distinct variable group(s):   ph,x   ph,y

Proof of Theorem 19.22dvv

Step	Hyp	Ref	Expression
1		19.20dvv.1	. . 3 |- (ph -> (ps -> ch))
2	1	19.22dv 947	. 2 |- (ph -> (E.yps -> E.ych))
3	2	19.22dv 947	1 |- (ph -> (E.xE.yps -> E.xE.ych))

Syntax hints:   -> wi 2  E.wex 678

This theorem is referenced by:  cgsex2g 1368  cgsex4g 1369  cla4e2gv 1398  th3q 3253

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-gen 677  ax-17 925

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

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