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Mirrors > Home > ILE Home > Th. List > pm3.2i | GIF version |
Description: Infer conjunction of premises. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
pm3.2i.1 | ⊢ 𝜑 |
pm3.2i.2 | ⊢ 𝜓 |
Ref | Expression |
---|---|
pm3.2i | ⊢ (𝜑 ∧ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.2i.1 | . 2 ⊢ 𝜑 | |
2 | pm3.2i.2 | . 2 ⊢ 𝜓 | |
3 | pm3.2 126 | . 2 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜓))) | |
4 | 1, 2, 3 | mp2 16 | 1 ⊢ (𝜑 ∧ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia3 101 |
This theorem is referenced by: mp4an 403 pm4.87 493 biijust 570 3pm3.2i 1082 sbequilem 1719 unssi 3118 ssini 3160 bm1.3ii 3878 epelg 4027 onsucelsucexmid 4255 elvv 4402 funpr 4951 mpt2v 5594 caovcom 5658 th3q 6211 endisj 6298 phplem2 6316 addnnnq0 6547 mulnnnq0 6548 nqprxx 6644 addsrpr 6830 mulsrpr 6831 recidpirq 6934 apreim 7594 mulcanapi 7648 div1 7680 recdivap 7694 divdivap1 7699 divdivap2 7700 divassapi 7744 divdirapi 7745 div23api 7746 div11api 7747 divmuldivapi 7748 divmul13api 7749 divadddivapi 7750 divdivdivapi 7751 lemulge11 7832 2cnne0 8134 2rene0 8135 1mhlfehlf 8143 halfpm6th 8145 2halves 8154 halfaddsub 8159 avglt1 8163 avglt2 8164 div4p1lem1div2 8177 nneoor 8340 zeo 8343 divlt1lt 8650 divle1le 8651 2tnp1ge0ge0 9143 frecfzennn 9203 expge1 9292 cjreb 9466 sqrt2gt1lt2 9647 amgm2 9714 ex-an 9894 ex-fl 9895 bdbm1.3ii 10011 |
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