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Theorem ax4 150
 Description: If is true for all , then it is true for . (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypothesis
Ref Expression
ax4.1
Assertion
Ref Expression
ax4

Proof of Theorem ax4
StepHypRef Expression
1 ax4.1 . . . 4
21wl 66 . . 3
3 wv 64 . . 3
42, 3ax4g 149 . 2
54ax-cb1 29 . . 3
61beta 92 . . 3
75, 6a1i 28 . 2
84, 7mpbi 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:  alimdv  184  alnex  186  ax5  207  ax7  209  ax10  213  axext  219
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