Theorem 19.32 1875

Description: Theorem 19.32 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)

Hypothesis

Ref	Expression
19.32.1	|- F/xph

Assertion

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

Proof of Theorem 19.32

Step	Hyp	Ref	Expression
1		19.32.1	. . . 4 |- F/xph
2	1	nfn 1793	. . 3 |- F/x -. ph
3	2	19.21 1796	. 2 |- (A.x(-. ph -> ps) <-> (-. ph -> A.xps))
4		df-or 359	. . 3 |- ((ph \/ ps) <-> (-. ph -> ps))
5	4	albii 1566	. 2 |- (A.x(ph \/ ps) <-> A.x(-. ph -> ps))
6		df-or 359	. 2 |- ((ph \/ A.xps) <-> (-. ph -> A.xps))
7	3, 5, 6	3bitr4i 268	1 |- (A.x(ph \/ ps) <-> (ph \/ A.xps))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   \/ wo 357  A.wal 1540   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-or 359  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  19.31  1876  2eu3  2286  axi12  2333