Theorem mpbidi 207

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 9-Aug-1994.)

Hypotheses

Ref	Expression
mpbidi.min	⊢ (θ → (φ → ψ))
mpbidi.maj	⊢ (φ → (ψ ↔ χ))

Assertion

Ref	Expression
mpbidi	⊢ (θ → (φ → χ))

Proof of Theorem mpbidi

Step	Hyp	Ref	Expression
1		mpbidi.min	. 2 ⊢ (θ → (φ → ψ))
2		mpbidi.maj	. . 3 ⊢ (φ → (ψ ↔ χ))
3	2	biimpd 198	. 2 ⊢ (φ → (ψ → χ))
4	1, 3	sylcom 25	1 ⊢ (θ → (φ → χ))

Syntax hints:   → wi 4   ↔ wb 176

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 177

This theorem is referenced by:  tpid3g  3832  ov3  5600  ovmpt4g  5711