Theorem 19.32v 1869

Description: Version of 19.32 2101 with a dv condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020.)

Assertion

Ref	Expression
19.32v	|- ( A. x ( ph \/ ps ) <-> ( ph \/ A. x ps ) )

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem 19.32v

Step	Hyp	Ref	Expression
1		19.21v 1868	. 2 |- ( A. x ( -. ph -> ps ) <-> ( -. ph -> A. x ps ) )
2		df-or 385	. . 3 |- ( ( ph \/ ps ) <-> ( -. ph -> ps ) )
3	2	albii 1747	. 2 |- ( A. x ( ph \/ ps ) <-> A. x ( -. ph -> ps ) )
4		df-or 385	. 2 |- ( ( ph \/ A. x ps ) <-> ( -. ph -> A. x ps ) )
5	1, 3, 4	3bitr4i 292	1 |- ( A. x ( ph \/ ps ) <-> ( ph \/ A. x ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705

This theorem is referenced by:  19.31v  1870  pm10.12  38557