Theorem 19.22dvv 1292

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 1290	. 2 |- (ph -> (E.yps -> E.ych))
3	2	19.22dv 1290	1 |- (ph -> (E.xE.yps -> E.xE.ych))

Syntax hints:   -> wi 3  E.wex 980

This theorem is referenced by:  cgsex2g 1832  cgsex4g 1833  cla42egv 1864  cla43egv 1866  relop 3275  th3q 4317

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-17 971  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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