Theorem disjmoOLD 4437

Description: Two ways to say that a collection () for is disjoint. (Contributed by Mario Carneiro, 26-Mar-2015.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
disjmo.1

Assertion

Ref	Expression
disjmoOLD

Distinct variable groups:   ,,,   ,,   ,,

Proof of Theorem disjmoOLD

Step	Hyp	Ref	Expression
1		dfdisj2 4424	. 2
2		disjmo.1	. . 3
3	2	disjor 4436	. 2
4	1, 3	bitr3i 251	1

Syntax hints:  ->wi 4  <->wb 184  \/wo 368  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  E*wmo 2283  A.wral 2807  i^icin 3474  c0 3784  Disj_wdisj 4422

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rmo 2815  df-v 3111  df-dif 3478  df-in 3482  df-nul 3785  df-disj 4423