Higher-Order Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HOLE Home  >  Th. List  >  cla4v Unicode version

Theorem cla4v 152
 Description: If is true for all , then it is true for . (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypotheses
Ref Expression
cla4v.1
cla4v.2
cla4v.3
Assertion
Ref Expression
cla4v
Distinct variable groups:   ,   ,   ,

Proof of Theorem cla4v
StepHypRef Expression
1 cla4v.1 . . . 4
21wl 66 . . 3
3 cla4v.2 . . 3
42, 3ax4g 149 . 2
54ax-cb1 29 . . 3
6 cla4v.3 . . . 4
71, 3, 6cl 116 . . 3
85, 7a1i 28 . 2
94, 8mpbi 82 1
 Colors of variables: type var term Syntax hints:  tv 1  hb 3  kc 5  kl 6   ke 7  kbr 9   wffMMJ2 11  wffMMJ2t 12  tal 122 This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-id 24  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-wctl 31  ax-wctr 32  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-ded 46  ax-wct 47  ax-wc 49  ax-ceq 51  ax-wv 63  ax-wl 65  ax-beta 67  ax-distrc 68  ax-leq 69  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80  ax-hbl1 103  ax-17 105  ax-inst 113 This theorem depends on definitions:  df-ov 73  df-al 126 This theorem is referenced by:  pm2.21  153  ecase  163  exlimdv2  166  ax4e  168  eta  178  exlimd  183  ac  197  ax10  213
 Copyright terms: Public domain W3C validator