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Theorem ax6 208
 Description: Axiom of Quantified Negation. Axiom C5-2 of [Monk2] p. 113. (Contributed by Mario Carneiro, 10-Oct-2014.)
Hypothesis
Ref Expression
ax6.1
Assertion
Ref Expression
ax6
Distinct variable group:   ,

Proof of Theorem ax6
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 wnot 138 . . 3
2 wal 134 . . . 4
3 ax6.1 . . . . 5
43wl 66 . . . 4
52, 4wc 50 . . 3
61, 5wc 50 . 2
7 wv 64 . . 3
81, 7ax-17 105 . . 3
92, 7ax-17 105 . . . 4
103, 7ax-hbl1 103 . . . 4
112, 4, 7, 9, 10hbc 110 . . 3
121, 5, 7, 8, 11hbc 110 . 2
136, 12isfree 188 1
 Colors of variables: type var term Syntax hints:  tv 1   ht 2  hb 3  kc 5  kl 6  kt 8  kbr 9   wffMMJ2 11  wffMMJ2t 12   tne 120   tim 121  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-distrl 70  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80  ax-hbl1 103  ax-17 105  ax-inst 113  ax-eta 177 This theorem depends on definitions:  df-ov 73  df-al 126  df-fal 127  df-an 128  df-im 129  df-not 130 This theorem is referenced by: (None)
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