Theorem iac 35

Description: & introduction rule. ax-iac 32 has a negation for some reason, this one doesn't.

Hypotheses

Ref	Expression
iac.1	⊦ (𝜑 ⅋ 𝜓)
iac.2	⊦ (𝜑 ⅋ 𝜒)

Assertion

Ref	Expression
iac	⊦ (𝜑 ⅋ (𝜓 & 𝜒))

Proof of Theorem iac

Step	Hyp	Ref	Expression
1		iac.1	. . . 4 ⊦ (𝜑 ⅋ 𝜓)
2	1	dni1 25	. . 3 ⊦ (~ ~ 𝜑 ⅋ 𝜓)
3		iac.2	. . . 4 ⊦ (𝜑 ⅋ 𝜒)
4	3	dni1 25	. . 3 ⊦ (~ ~ 𝜑 ⅋ 𝜒)
5	2, 4	ax-iac 32	. 2 ⊦ (~ ~ 𝜑 ⅋ (𝜓 & 𝜒))
6	5	dne1 26	1 ⊦ (𝜑 ⅋ (𝜓 & 𝜒))

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-iac 32

This theorem is referenced by:  iaci  36  acco  43  acas  44  acasr  45  dismdac  46  extmdac  47  acm1  80