Theorem 19.28 1068

Description: Theorem 19.28 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.28.1	|- (ph -> A.xph)

Assertion

Ref	Expression
19.28	|- (A.x(ph /\ ps) <-> (ph /\ A.xps))

Proof of Theorem 19.28

Step	Hyp	Ref	Expression
1		19.26 1065	. 2 |- (A.x(ph /\ ps) <-> (A.xph /\ A.xps))
2		19.28.1	. . . 4 |- (ph -> A.xph)
3	2	19.3 1029	. . 3 |- (A.xph <-> ph)
4	3	anbi1i 481	. 2 |- ((A.xph /\ A.xps) <-> (ph /\ A.xps))
5	1, 4	bitr 173	1 |- (A.x(ph /\ ps) <-> (ph /\ A.xps))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223  A.wal 952

This theorem is referenced by:  aaan 1117  19.28v 1297  cbval2 1314

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-4 971  ax-5o 973

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

Copyright terms: Public domain