Theorem bamalipOLD 2787

Description: Obsolete proof of bamalip 2786 as of 16-Sep-2022. (Contributed by David A. Wheeler, 28-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bamalip.maj	⊢ ∀𝑥(𝜑 → 𝜓)
bamalip.min	⊢ ∀𝑥(𝜓 → 𝜒)
bamalip.e	⊢ ∃𝑥𝜑

Assertion

Ref	Expression
bamalipOLD	⊢ ∃𝑥(𝜒 ∧ 𝜑)

Proof of Theorem bamalipOLD

Step	Hyp	Ref	Expression
1		bamalip.e	. 2 ⊢ ∃𝑥𝜑
2		bamalip.maj	. . . . 5 ⊢ ∀𝑥(𝜑 → 𝜓)
3	2	spi 2227	. . . 4 ⊢ (𝜑 → 𝜓)
4		bamalip.min	. . . . 5 ⊢ ∀𝑥(𝜓 → 𝜒)
5	4	spi 2227	. . . 4 ⊢ (𝜓 → 𝜒)
6	3, 5	syl 17	. . 3 ⊢ (𝜑 → 𝜒)
7	6	ancri 547	. 2 ⊢ (𝜑 → (𝜒 ∧ 𝜑))
8	1, 7	eximii 1937	1 ⊢ ∃𝑥(𝜒 ∧ 𝜑)

Syntax hints:   → wi 4   ∧ wa 386  ∀wal 1656  ∃wex 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-12 2222

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1881

This theorem is referenced by: (None)