Theorem 19.22dvv 1294

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 groups:   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 1292	. 2 |- (ph -> (E.yps -> E.ych))
3	2	19.22dv 1292	1 |- (ph -> (E.xE.yps -> E.xE.ych))

Syntax hints:   -> wi 3  E.wex 982

This theorem is referenced by:  cgsex2g 1835  cgsex4g 1836  cla42egv 1867  cla43egv 1869  relop 3282  th3q 4324

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-17 973  ax-4 975  ax-5o 977

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983

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