Theorem 19.27 1069

Description: Theorem 19.27 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.27.1	|- (ps -> A.xps)

Assertion

Ref	Expression
19.27	|- (A.x(ph /\ ps) <-> (A.xph /\ ps))

Proof of Theorem 19.27

Step	Hyp	Ref	Expression
1		19.26 1067	. 2 |- (A.x(ph /\ ps) <-> (A.xph /\ A.xps))
2		19.27.1	. . . 4 |- (ps -> A.xps)
3	2	19.3 1031	. . 3 |- (A.xps <-> ps)
4	3	anbi2i 480	. 2 |- ((A.xph /\ A.xps) <-> (A.xph /\ ps))
5	1, 4	bitr 173	1 |- (A.x(ph /\ ps) <-> (A.xph /\ ps))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223  A.wal 954

This theorem is referenced by:  exan 1106  aaan 1119  19.27v 1298

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

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

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