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Mirrors > Home > HOLE Home > Th. List > ax10 | Unicode version |
Description: Axiom of Quantifier Substitution. Appears as Lemma L12 in [Megill] p. 445 (p. 12 of the preprint). |
Ref | Expression |
---|---|
ax10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wv 58 | . . . . . 6 | |
2 | wv 58 | . . . . . . . 8 | |
3 | wv 58 | . . . . . . . 8 | |
4 | 2, 3 | weqi 68 | . . . . . . 7 |
5 | weq 38 | . . . . . . . 8 | |
6 | 5, 2, 1 | wov 64 | . . . . . . . . 9 |
7 | 6 | id 25 | . . . . . . . 8 |
8 | 5, 2, 3, 7 | oveq1 89 | . . . . . . 7 |
9 | 4, 1, 8 | cla4v 142 | . . . . . 6 |
10 | 4 | ax4 140 | . . . . . . 7 |
11 | 2, 10 | eqcomi 70 | . . . . . 6 |
12 | 1, 9, 11 | eqtri 85 | . . . . 5 |
13 | 12 | alrimiv 141 | . . . 4 |
14 | wal 124 | . . . . . 6 | |
15 | 4 | wl 59 | . . . . . 6 |
16 | 14, 15 | wc 45 | . . . . 5 |
17 | 3, 2 | weqi 68 | . . . . . . 7 |
18 | 17 | wl 59 | . . . . . 6 |
19 | 3, 1 | weqi 68 | . . . . . . . . 9 |
20 | 19 | id 25 | . . . . . . . 8 |
21 | 5, 3, 2, 20 | oveq1 89 | . . . . . . 7 |
22 | 17, 21 | cbv 168 | . . . . . 6 |
23 | 14, 18, 22 | ceq2 80 | . . . . 5 |
24 | 16, 23 | a1i 28 | . . . 4 |
25 | 13, 24 | mpbir 77 | . . 3 |
26 | wtru 40 | . . 3 | |
27 | 25, 26 | adantl 51 | . 2 |
28 | 27 | ex 148 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 ht 2 hb 3 kc 5 kl 6 ke 7 kt 8 kbr 9 wffMMJ2 11 tim 111 tal 112 |
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-refl 39 ax-eqmp 42 ax-ded 43 ax-ceq 46 ax-beta 60 ax-distrc 61 ax-leq 62 ax-distrl 63 ax-hbl1 93 ax-17 95 ax-inst 103 ax-eta 165 |
This theorem depends on definitions: df-ov 65 df-al 116 df-an 118 df-im 119 |
This theorem is referenced by: (None) |
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