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Mirrors > Home > NFE Home > Th. List > anim12ci | GIF version |
Description: Variant of anim12i 549 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
anim12i.1 | ⊢ (φ → ψ) |
anim12i.2 | ⊢ (χ → θ) |
Ref | Expression |
---|---|
anim12ci | ⊢ ((φ ∧ χ) → (θ ∧ ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anim12i.2 | . . 3 ⊢ (χ → θ) | |
2 | anim12i.1 | . . 3 ⊢ (φ → ψ) | |
3 | 1, 2 | anim12i 549 | . 2 ⊢ ((χ ∧ φ) → (θ ∧ ψ)) |
4 | 3 | ancoms 439 | 1 ⊢ ((φ ∧ χ) → (θ ∧ ψ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 |
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 df-an 360 |
This theorem is referenced by: 2exeu 2281 frecxp 6314 |
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