Theorem 19.31v 1870

Description: Version of 19.31 2102 with a dv condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020.)

Assertion

Ref	Expression
19.31v	|- ( A. x ( ph \/ ps ) <-> ( A. x ph \/ ps ) )

Distinct variable group:   ps, x

Allowed substitution hint:   ph( x)

Proof of Theorem 19.31v

Step	Hyp	Ref	Expression
1		19.32v 1869	. 2 |- ( A. x ( ps \/ ph ) <-> ( ps \/ A. x ph ) )
2		orcom 402	. . 3 |- ( ( ph \/ ps ) <-> ( ps \/ ph ) )
3	2	albii 1747	. 2 |- ( A. x ( ph \/ ps ) <-> A. x ( ps \/ ph ) )
4		orcom 402	. 2 |- ( ( A. x ph \/ ps ) <-> ( ps \/ A. x ph ) )
5	1, 3, 4	3bitr4i 292	1 |- ( A. x ( ph \/ ps ) <-> ( A. x ph \/ ps ) )

Syntax hints:   <-> 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:  19.31vv  38583