eupth2lem1 - Intuitionistic Logic Explorer

	Intuitionistic Logic Explorer		< Previous Next > Nearby theorems
Mirrors > Home > ILE Home > Th. List > eupth2lem1		Unicode version

Theorem eupth2lem1 16308

Description: Lemma for eupth2 . (Contributed by Mario Carneiro, 8-Apr-2015.)

**Assertion**
Ref	Expression
eupth2lem1	$/\$ $\/$

**Proof of Theorem eupth2lem1**
Step	Hyp	Ref	Expression
1		elif 3617	. . 3 $/\$ $\/$ $/\$
2		noel 3498	. . . . 5
3	2	intnan 936	. . . 4 $/\$
4		biorf 751	. . . 4 $/\$ $/\$ $/\$ $\/$ $/\$
5	3, 4	ax-mp 5	. . 3 $/\$ $/\$ $\/$ $/\$
6	1, 5	bitr4i 187	. 2 $/\$
7		df-ne 2403	. . . . 5
8	7	bicomi 132	. . . 4
9	8	a1i 9	. . 3
10		elprg 3689	. . 3 $\/$
11	9, 10	anbi12d 473	. 2 $/\$ $/\$ $\/$
12	6, 11	bitrid 192	1 $/\$ $\/$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 104

wb 105 $\/$ wo 715

wceq 1397

wcel 2202

wne 2402

c0 3494

cif 3605

cpr 3670

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 619 ax-in2 620 ax-io 716 ax-5 1495 ax-7 1496 ax-gen 1497 ax-ie1 1541 ax-ie2 1542 ax-8 1552 ax-10 1553 ax-11 1554 ax-i12 1555 ax-bndl 1557 ax-4 1558 ax-17 1574 ax-i9 1578 ax-ial 1582 ax-i5r 1583 ax-ext 2213

This theorem depends on definitions: df-bi 117 df-tru 1400 df-nf 1509 df-sb 1811 df-clab 2218 df-cleq 2224 df-clel 2227 df-nfc 2363 df-ne 2403 df-v 2804 df-dif 3202 df-un 3204 df-nul 3495 df-if 3606 df-sn 3675 df-pr 3676

This theorem is referenced by: eupth2lem2dc 16309