Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > simp3r | GIF version |
Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.) |
Ref | Expression |
---|---|
simp3r | ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 108 | . 2 ⊢ ((𝜒 ∧ 𝜃) → 𝜃) | |
2 | 1 | 3ad2ant3 961 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 ∧ w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: simpl3r 994 simpr3r 1000 simp13r 1054 simp23r 1060 simp33r 1066 issod 4074 tfisi 4328 fvun1 5260 f1oiso2 5486 tfrlem5 5953 ecopovtrn 6226 ecopovtrng 6229 addassnqg 6572 ltsonq 6588 ltanqg 6590 ltmnqg 6591 addassnq0 6652 mulasssrg 6935 distrsrg 6936 lttrsr 6939 ltsosr 6941 ltasrg 6947 mulextsr1lem 6956 mulextsr1 6957 axmulass 7039 axdistr 7040 reapmul1 7695 mulcanap 7755 mulcanap2 7756 divassap 7778 divdirap 7785 div11ap 7788 apmul1 7876 ltdiv1 7946 ltmuldiv 7952 ledivmul 7955 lemuldiv 7959 lediv2 7969 ltdiv23 7970 lediv23 7971 modqdi 9394 expaddzap 9520 expmulzap 9522 resqrtcl 9915 dvdsgcd 10401 rpexp12i 10534 |
Copyright terms: Public domain | W3C validator |