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Mirrors > Home > HOLE Home > Th. List > ax2 | Unicode version |
Description: Axiom Frege. Axiom A2 of [Margaris] p. 49. |
Ref | Expression |
---|---|
ax1.1 | |
ax1.2 | |
ax2.3 |
Ref | Expression |
---|---|
ax2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax2.3 | . . . . . 6 | |
2 | ax1.2 | . . . . . . 7 | |
3 | wim 127 | . . . . . . . . . 10 | |
4 | ax1.1 | . . . . . . . . . 10 | |
5 | 3, 2, 1 | wov 64 | . . . . . . . . . 10 |
6 | 3, 4, 5 | wov 64 | . . . . . . . . 9 |
7 | 3, 4, 2 | wov 64 | . . . . . . . . 9 |
8 | 6, 7 | wct 44 | . . . . . . . 8 |
9 | 8, 4 | simpr 23 | . . . . . . 7 |
10 | 8, 4 | simpl 22 | . . . . . . . 8 |
11 | 10 | simprd 36 | . . . . . . 7 |
12 | 2, 9, 11 | mpd 146 | . . . . . 6 |
13 | 10 | simpld 35 | . . . . . . 7 |
14 | 5, 9, 13 | mpd 146 | . . . . . 6 |
15 | 1, 12, 14 | mpd 146 | . . . . 5 |
16 | 15 | ex 148 | . . . 4 |
17 | 16 | ex 148 | . . 3 |
18 | wtru 40 | . . 3 | |
19 | 17, 18 | adantl 51 | . 2 |
20 | 19 | ex 148 | 1 |
Colors of variables: type var term |
Syntax hints: hb 3 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) |
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