Higher-Order Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HOLE Home  >  Th. List  >  ax4g Unicode version

Theorem ax4g 149
 Description: If is true for all , then it is true for . (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypotheses
Ref Expression
ax4g.1
ax4g.2
Assertion
Ref Expression
ax4g

Proof of Theorem ax4g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 wal 134 . . . 4
2 ax4g.1 . . . 4
31, 2wc 50 . . 3
43trud 27 . 2
5 ax4g.2 . . . 4
62, 5wc 50 . . 3
74ax-cb1 29 . . . . . 6
87id 25 . . . . 5
92alval 142 . . . . . 6
107, 9a1i 28 . . . . 5
118, 10mpbi 82 . . . 4
122, 5, 11ceq1 89 . . 3
135, 4hbth 109 . . 3
146, 12, 13eqtri 95 . 2
154, 14mpbir 87 1
 Colors of variables: type var term Syntax hints:   ht 2  hb 3  kc 5  kl 6   ke 7  kt 8  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:  ax4  150  cla4v  152
 Copyright terms: Public domain W3C validator