Theorem simp3r2 1283

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp3r2	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Proof of Theorem simp3r2

Step	Hyp	Ref	Expression
1		simpr2 1196	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1135	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088

This theorem is referenced by:  nllyrest  23424  cdlemblem  39812  cdleme21  40356  cdleme22b  40360  cdleme40m  40486  cdlemg34  40731  cdlemk5u  40880  cdlemk6u  40881  cdlemk21N  40892  cdlemk20  40893  cdlemk26b-3  40924  cdlemk26-3  40925  cdlemk28-3  40927  cdlemky  40945  cdlemk11t  40965  cdlemkyyN  40981  stoweidlem56  46085