Theorem alloverimex-P5.RC 602

Description: Inference Form of alloverimex-P5 601.

Hypothesis

Ref	Expression
alloverimex-P5.RC.1	⊢ ∀𝑥(𝜑 → 𝜓)

Assertion

Ref	Expression
alloverimex-P5.RC	⊢ (∃𝑥𝜑 → ∃𝑥𝜓)

Proof of Theorem alloverimex-P5.RC

Step	Hyp	Ref	Expression
1		alloverimex-P5.RC.1	. . . 4 ⊢ ∀𝑥(𝜑 → 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ∀𝑥(𝜑 → 𝜓))
3	2	alloverimex-P5 601	. 2 ⊢ (⊤ → (∃𝑥𝜑 → ∃𝑥𝜓))
4	3	ndtruee-P3.18 183	1 ⊢ (∃𝑥𝜑 → ∃𝑥𝜓)

Syntax hints:  ∀wff-forall 8   → wff-imp 10  ⊤wff-true 153  ∃wff-exists 595

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161  df-exists-D5.1 596

This theorem is referenced by:  alloverimex-P5.RC.GEN  603