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Mirrors > Home > ILE Home > Th. List > ad2ant2lr | GIF version |
Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 23-Nov-2007.) |
Ref | Expression |
---|---|
ad2ant2.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
ad2ant2lr | ⊢ (((𝜃 ∧ 𝜑) ∧ (𝜓 ∧ 𝜏)) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant2.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | adantrr 479 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜏)) → 𝜒) |
3 | 2 | adantll 476 | 1 ⊢ (((𝜃 ∧ 𝜑) ∧ (𝜓 ∧ 𝜏)) → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem is referenced by: mpteqb 5606 fiunsnnn 6880 addcomnqg 7379 addassnqg 7380 nqtri3or 7394 lt2addnq 7402 lt2mulnq 7403 enq0ref 7431 enq0tr 7432 nqnq0pi 7436 nqpnq0nq 7451 nqnq0a 7452 distrnq0 7457 addassnq0lemcl 7459 ltsrprg 7745 mulcomsrg 7755 mulasssrg 7756 distrsrg 7757 aptisr 7777 mulcnsr 7833 cnegex 8134 sub4 8201 muladd 8340 ltleadd 8402 divdivdivap 8669 divadddivap 8683 ltmul12a 8816 fzrev 10083 facndiv 10718 cncongr1 12102 blbas 13903 cncfmet 14049 ptolemy 14215 |
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