Theorem 19.20i2 969

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 968	. 2 |- (A.yph -> A.yps)
3	2	19.20i 968	1 |- (A.xA.yph -> A.xA.yps)

Syntax hints:   -> wi 3  A.wal 950

This theorem is referenced by:  dvelimdf 1235  mo 1370  2mo 1424  2eu6 1431  hbabd 1445  tz7.48lem 3894  fnoprabg 3951  axacndlem4 4885

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

Copyright terms: Public domain