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Mirrors > Home > HOLE Home > Th. List > ax1 | GIF version |
Description: Axiom Simp. Axiom A1 of [Margaris] p. 49. |
Ref | Expression |
---|---|
ax1.1 | ⊢ R:∗ |
ax1.2 | ⊢ S:∗ |
Ref | Expression |
---|---|
ax1 | ⊢ ⊤⊧[R ⇒ [S ⇒ R]] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wtru 40 | . . . . 5 ⊢ ⊤:∗ | |
2 | ax1.1 | . . . . 5 ⊢ R:∗ | |
3 | 1, 2 | simpr 23 | . . . 4 ⊢ (⊤, R)⊧R |
4 | ax1.2 | . . . 4 ⊢ S:∗ | |
5 | 3, 4 | adantr 50 | . . 3 ⊢ ((⊤, R), S)⊧R |
6 | 5 | ex 148 | . 2 ⊢ (⊤, R)⊧[S ⇒ R] |
7 | 6 | ex 148 | 1 ⊢ ⊤⊧[R ⇒ [S ⇒ R]] |
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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