Theorem eac1d 37

Description: & elimination rule, left hand side. ax-eac1 33 has a negation for some reason, this one doesn't.

Hypothesis

Ref	Expression
eac1d.1	⊦ (𝜑 ⅋ (𝜓 & 𝜒))

Assertion

Ref	Expression
eac1d	⊦ (𝜑 ⅋ 𝜓)

Proof of Theorem eac1d

Step	Hyp	Ref	Expression
1		eac1d.1	. . . 4 ⊦ (𝜑 ⅋ (𝜓 & 𝜒))
2	1	dni1 25	. . 3 ⊦ (~ ~ 𝜑 ⅋ (𝜓 & 𝜒))
3	2	ax-eac1 33	. 2 ⊦ (~ ~ 𝜑 ⅋ 𝜓)
4	3	dne1 26	1 ⊦ (𝜑 ⅋ 𝜓)

Syntax hints:   ⅋ wmd 2  ~ wneg 3   & wac 30

This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-eac1 33

This theorem is referenced by:  acco  43  acas  44  acasr  45  dismdac  46  extmdac  47  acm1  80  abs1  178