Theorem bnj240 35097

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 1150	. . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜓′)
3		bnj240.2	. . . 4 ⊢ (𝜒 → 𝜒′)
4	3	3ad2ant2 1151	. . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜒′)
5	2, 4	jca 520	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → (𝜓′ ∧ 𝜒′))
6	5	3comr 1142	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓′ ∧ 𝜒′))

This proof depends on syntax axioms:   → wi 4   ∧ wa 400   ∧ w3a 1102

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-3an 1104

This theorem is used by:  bnj594  35309  bnj580  35310  bnj966  35341  bnj967  35342