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Theorem cdleme31sn1c 30874
 Description: Part of proof of Lemma E in [Crawley] p. 113. (Contributed by NM, 1-Mar-2013.)
Hypotheses
Ref Expression
cdleme31sn1c.g
cdleme31sn1c.i
cdleme31sn1c.n
cdleme31sn1c.y
cdleme31sn1c.c
Assertion
Ref Expression
cdleme31sn1c
Distinct variable groups:   ,,,   ,   ,   ,,,   ,,,   ,   ,,,   ,,,   ,,,   ,
Allowed substitution hints:   (,)   (,,)   (,,)   (,)   (,,)   (,,)   (,)   (,,)   (,)   (,,)

Proof of Theorem cdleme31sn1c
StepHypRef Expression
1 cdleme31sn1c.i . . 3
2 cdleme31sn1c.n . . 3
3 eqid 2408 . . 3
41, 2, 3cdleme31sn1 30867 . 2
5 cdleme31sn1c.g . . . . . . . . 9
6 cdleme31sn1c.y . . . . . . . . 9
75, 6cdleme31se 30868 . . . . . . . 8
87adantr 452 . . . . . . 7
98eqeq2d 2419 . . . . . 6
109imbi2d 308 . . . . 5
1110ralbidv 2690 . . . 4
1211riotabidv 6514 . . 3
13 cdleme31sn1c.c . . 3
1412, 13syl6eqr 2458 . 2
154, 14eqtrd 2440 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   wceq 1649   wcel 1721  wral 2670  csb 3215  cif 3703   class class class wbr 4176  (class class class)co 6044  crio 6505 This theorem is referenced by:  cdlemefs32sn1aw  30900  cdleme43fsv1snlem  30906  cdleme41sn3a  30919  cdleme40m  30953  cdleme40n  30954 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2262  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ral 2675  df-rex 2676  df-reu 2677  df-rab 2679  df-v 2922  df-sbc 3126  df-csb 3216  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-op 3787  df-uni 3980  df-br 4177  df-iota 5381  df-fv 5425  df-ov 6047  df-riota 6512
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