Higher-Order Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > HOLE Home > Th. List > ax14 | Unicode version |
Description: Axiom of Equality. Axiom scheme C12' in [Megill] p. 448 (p. 16 of the preprint). It is a special case of Axiom B8 (p. 75) of system S2 of [Tarski] p. 77. |
Ref | Expression |
---|---|
ax14.1 | |
ax14.2 | |
ax14.3 |
Ref | Expression |
---|---|
ax14 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wtru 40 | . . . . . 6 | |
2 | ax14.1 | . . . . . . 7 | |
3 | ax14.2 | . . . . . . 7 | |
4 | 2, 3 | weqi 68 | . . . . . 6 |
5 | 1, 4 | wct 44 | . . . . 5 |
6 | ax14.3 | . . . . . 6 | |
7 | 2, 6 | wc 45 | . . . . 5 |
8 | 5, 7 | simpr 23 | . . . 4 |
9 | 1, 4 | simpr 23 | . . . . . 6 |
10 | 2, 6, 9 | ceq1 79 | . . . . 5 |
11 | 10, 7 | adantr 50 | . . . 4 |
12 | 8, 11 | mpbi 72 | . . 3 |
13 | 12 | ex 148 | . 2 |
14 | 13 | ex 148 | 1 |
Colors of variables: type var term |
Syntax hints: ht 2 hb 3 kc 5 ke 7 kt 8 kbr 9 kct 10 wffMMJ2 11 wffMMJ2t 12 tim 111 |
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 |
This theorem depends on definitions: df-ov 65 df-an 118 df-im 119 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |