Theorem mtbird 537

Description: A deduction from a biconditional, similar to modus tollens.

Hypotheses

Ref	Expression
mtbird.min	⊢ (φ → ¬ χ)
mtbird.maj	⊢ (φ → (ψ ↔ χ))

Assertion

Ref	Expression
mtbird	⊢ (φ → ¬ ψ)

Proof of Theorem mtbird

Step	Hyp	Ref	Expression
1		mtbird.min	. 2 ⊢ (φ → ¬ χ)
2		mtbird.maj	. . 3 ⊢ (φ → (ψ ↔ χ))
3	2	biimpd 135	. 2 ⊢ (φ → (ψ → χ))
4	1, 3	mtod 95	1 ⊢ (φ → ¬ ψ)

Syntax hints:  ¬ wn 1   → wi 2   ↔ wb 127

This theorem is referenced by:  php 3409  onomeneq 3414  rankr1 3518  cardnn 3631  cardaleph 3690  addnidpi 3822  zbtwnre 4619  znnenlem 4929  strlem1 5691

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

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