Theorem bnj240 32578

Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bnj240.1	⊢ (𝜓 → 𝜓′)
bnj240.2	⊢ (𝜒 → 𝜒′)

Assertion

Ref	Expression
bnj240	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓′ ∧ 𝜒′))

Proof of Theorem bnj240

Step	Hyp	Ref	Expression
1		bnj240.1	. . . 4 ⊢ (𝜓 → 𝜓′)
2	1	3ad2ant1 1131	. . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜓′)
3		bnj240.2	. . . 4 ⊢ (𝜒 → 𝜒′)
4	3	3ad2ant2 1132	. . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜒′)
5	2, 4	jca 511	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → (𝜓′ ∧ 𝜒′))
6	5	3comr 1123	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓′ ∧ 𝜒′))

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

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 396  df-3an 1087

This theorem is referenced by:  bnj594  32792  bnj580  32793  bnj966  32824  bnj967  32825