Theorem 19.21 1545

Description: Theorem 19.21 of [Margaris] p. 90. The hypothesis can be thought of as " x is not free in ph." (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)

Hypothesis

Ref	Expression
19.21.1	|- F/ x ph

Assertion

Ref	Expression
19.21	|- ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) )

Proof of Theorem 19.21

Step	Hyp	Ref	Expression
1		19.21.1	. 2 |- F/ x ph
2		19.21t 1544	. 2 |- ( F/ x ph -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )
3	1, 2	ax-mp 7	1 |- ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1312   F/wnf 1419

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-4 1470  ax-ial 1497  ax-i5r 1498

This theorem depends on definitions:  df-bi 116  df-nf 1420

This theorem is referenced by:  stdpc5  1546  19.21-2  1628  19.32dc  1640  cbv1  1705  eu2  2019  mo3h  2028  moanim  2049  r2alf  2426