Theorem mpan2i 522

Description: An inference based on modus ponens.

Hypotheses

Ref	Expression
mpan2i.1	⊢ χ
mpan2i.2	⊢ (φ → ((ψ ∧ χ) → θ))

Assertion

Ref	Expression
mpan2i	⊢ (φ → (ψ → θ))

Proof of Theorem mpan2i

Step	Hyp	Ref	Expression
1		mpan2i.1	. 2 ⊢ χ
2		mpan2i.2	. . 3 ⊢ (φ → ((ψ ∧ χ) → θ))
3	2	exp3a 292	. 2 ⊢ (φ → (ψ → (χ → θ)))
4	1, 3	mpii 45	1 ⊢ (φ → (ψ → θ))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  mpan22 532  fr2nr 2177  fr3nr 2178  sdomsdomcard 3654  cflecard 3707  genpprecl 3898  nnleltp1t 4448  nominpos 4509  lt0nnn0 4549  sqrlem6 4736  sqrlem12 4742  sqr00t 4770

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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