7p4e11 - Intuitionistic Logic Explorer

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Theorem 7p4e11 8952

Description: 7 + 4 = 11. (Contributed by Mario Carneiro, 19-Apr-2015.) (Revised by AV, 6-Sep-2021.)

**Assertion**
Ref	Expression
7p4e11	;

**Proof of Theorem 7p4e11**
Step	Hyp	Ref	Expression
1		7nn0 8695	. 2
2		3nn0 8691	. 2
3		0nn0 8688	. 2
4		df-4 8483	. 2
5		1e0p1 8918	. 2
6		7p3e10 8951	. 2 ;
7	1, 2, 3, 4, 5, 6	6p5lem 8946	1 ;

Colors of variables: wff set class

Syntax hints:

wceq 1289 (class class class)co 5652

cc0 7350

c1 7351

caddc 7353

c3 8474

c4 8475

c7 8478 ;cdc 8877

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 ax-setind 4353 ax-cnex 7436 ax-resscn 7437 ax-1cn 7438 ax-1re 7439 ax-icn 7440 ax-addcl 7441 ax-addrcl 7442 ax-mulcl 7443 ax-addcom 7445 ax-mulcom 7446 ax-addass 7447 ax-mulass 7448 ax-distr 7449 ax-i2m1 7450 ax-1rid 7452 ax-0id 7453 ax-rnegex 7454 ax-cnre 7456

This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-ral 2364 df-rex 2365 df-reu 2366 df-rab 2368 df-v 2621 df-sbc 2841 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-int 3689 df-br 3846 df-opab 3900 df-id 4120 df-xp 4444 df-rel 4445 df-cnv 4446 df-co 4447 df-dm 4448 df-iota 4980 df-fun 5017 df-fv 5023 df-riota 5608 df-ov 5655 df-oprab 5656 df-mpt2 5657 df-sub 7655 df-inn 8423 df-2 8481 df-3 8482 df-4 8483 df-5 8484 df-6 8485 df-7 8486 df-8 8487 df-9 8488 df-n0 8674 df-dec 8878

This theorem is referenced by: 7p5e12 8953 7t3e21 8986