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Theorem ax172 28343
Description: Quantification of two variables over a formula in which they do not occur. (Contributed by Alan Sare, 12-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax172  |-  ( ph  ->  A. x A. y ph )
Distinct variable group:    ph, x, y

Proof of Theorem ax172
StepHypRef Expression
1 ax-17 1603 . 2  |-  ( ph  ->  A. y ph )
2 ax-17 1603 . 2  |-  ( A. y ph  ->  A. x A. y ph )
31, 2syl 15 1  |-  ( ph  ->  A. x A. y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-17 1603
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