Theorem simp33l 1297

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

Assertion

Ref	Expression
simp33l	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

Proof of Theorem simp33l

Step	Hyp	Ref	Expression
1		simp3l 1198	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2ant3 1132	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 394   ∧ w3a 1084

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 206  df-an 395  df-3an 1086

This theorem is referenced by:  totprob  34198  cdleme19b  39927  cdleme19d  39929  cdleme19e  39930  cdleme20h  39939  cdleme20l2  39944  cdleme20m  39946  cdleme21d  39953  cdleme21e  39954  cdleme22e  39967  cdleme22f2  39970  cdleme22g  39971  cdleme26e  39982  cdleme28a  39993  cdleme28b  39994  cdleme37m  40085  cdleme39n  40089  cdlemeg46gfre  40155  cdlemg28a  40316  cdlemg28b  40326  cdlemk3  40456  cdlemk5a  40458  cdlemk6  40460  cdlemkuat  40489  cdlemkid2  40547