rp-fakeanorass - Mathbox for Richard Penner

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Theorem rp-fakeanorass 37858

Description: A special case where a mixture of and and or appears to conform to a mixed associative law. (Contributed by Richard Penner, 26-Feb-2020.)

**Assertion**
Ref	Expression
rp-fakeanorass	$/\$ $\/$ $/\$ $\/$

**Proof of Theorem rp-fakeanorass**
Step	Hyp	Ref	Expression
1		pm1.4 401	. . . . . . . 8 $\/$ $\/$
2	1	ord 392	. . . . . . 7 $\/$
3		pm4.83 970	. . . . . . . 8 $/\$
4	3	biimpi 206	. . . . . . 7 $/\$
5	2, 4	sylan2 491	. . . . . 6 $/\$ $\/$
6	5	ex 450	. . . . 5 $\/$
7	6	anim1d 588	. . . 4 $\/$ $/\$ $\/$ $/\$ $\/$
8		orc 400	. . . . 5 $\/$
9	8	anim1i 592	. . . 4 $/\$ $\/$ $\/$ $/\$ $\/$
10	7, 9	jctir 561	. . 3 $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $/\$ $\/$ $\/$ $/\$ $\/$
11		olc 399	. . . . . 6 $\/$
12		olc 399	. . . . . 6 $\/$
13	11, 12	jca 554	. . . . 5 $\/$ $/\$ $\/$
14		simpl 473	. . . . 5 $/\$ $\/$
15	13, 14	imim12i 62	. . . 4 $\/$ $/\$ $\/$ $/\$ $\/$
16	15	adantr 481	. . 3 $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $/\$ $\/$ $\/$ $/\$ $\/$
17	10, 16	impbii 199	. 2 $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $/\$ $\/$ $\/$ $/\$ $\/$
18		dfbi2 660	. 2 $\/$ $/\$ $\/$ $/\$ $\/$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $/\$ $\/$ $\/$ $/\$ $\/$
19		ordir 909	. . . 4 $/\$ $\/$ $\/$ $/\$ $\/$
20	19	bicomi 214	. . 3 $\/$ $/\$ $\/$ $/\$ $\/$
21	20	bibi1i 328	. 2 $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$
22	17, 18, 21	3bitr2i 288	1 $/\$ $\/$ $/\$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4

wb 196 $\/$ wo 383 $/\$ wa 384

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8

This theorem depends on definitions: df-bi 197 df-or 385 df-an 386

This theorem is referenced by: rp-fakeoranass 37859 rp-fakeinunass 37861

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