Theorem 19.20i2 993

Description: Inference doubly quantifying both antecedent and consequent.

Hypothesis

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

Assertion

Ref	Expression
19.20i2	|- (A.xA.yph -> A.xA.yps)

Proof of Theorem 19.20i2

Step	Hyp	Ref	Expression
1		19.20i.1	. . 3 |- (ph -> ps)
2	1	19.20i 992	. 2 |- (A.yph -> A.yps)
3	2	19.20i 992	1 |- (A.xA.yph -> A.xA.yps)

Syntax hints:   -> wi 3  A.wal 954

This theorem is referenced by:  dvelimdf 1251  mo 1393  2mo 1447  2eu6 1454  hbabd 1468  tz7.48lem 3955  fnoprabg 4012  axacndlem4 4962

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

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