Theorem 19.31 2102

Description: Theorem 19.31 of [Margaris] p. 90. See 19.31v 1870 for a version requiring fewer axioms. (Contributed by NM, 14-May-1993.)

Hypothesis

Ref	Expression
19.31.1	|- F/ x ps

Assertion

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

Proof of Theorem 19.31

Step	Hyp	Ref	Expression
1		19.31.1	. . 3 |- F/ x ps
2	1	19.32 2101	. 2 |- ( A. x ( ps \/ ph ) <-> ( ps \/ A. x ph ) )
3		orcom 402	. . 3 |- ( ( ph \/ ps ) <-> ( ps \/ ph ) )
4	3	albii 1747	. 2 |- ( A. x ( ph \/ ps ) <-> A. x ( ps \/ ph ) )
5		orcom 402	. 2 |- ( ( A. x ph \/ ps ) <-> ( ps \/ A. x ph ) )
6	2, 4, 5	3bitr4i 292	1 |- ( A. x ( ph \/ ps ) <-> ( A. x ph \/ ps ) )

Syntax hints:   <-> wb 196   \/ wo 383   A.wal 1481   F/wnf 1708

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  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by:  2eu3  2555